There is a lot of Misinformation related to the Archaeological facts about The Temple Mount

I finally started to just read some stuff from those who defend the official mainstream position.  And the people wanting to remove The Temple from the Mount altogether are misrepresenting a lot of facts especially in regards to the Antonia Fortress.

Wherever Antonia was it certainly wasn't the entirety of the Temple Mount.  And it probably may not have been where Jesus was tried before Pilate, and there are etymological issues with identifying the Gabbatha of John 19 with a Rock like the Dome of The Rock's.

One thing I've been noticing for awhile in those supporting the Gihon Spring or Nea Church location flat out ignore Hadrian's Temple to Jupiter when discussing the history since they want to claim nothing else was ever built on the same site.  We know even from a secular pagan gentile source that Hadrain did that, Cassius Dio.  And Jerome says the Statue of Hadrian standing over the Holy of Holies was still there in his day. Jerome identifies it with the Abomination of Desolation of Matthew 24 but still clearly had a Futurist understanding of Revelation.  For that eschatologically influenced reason he might be off on it being exactly where the Holy of Holies was, many think Antiochus's AoD was in the Holy of Holies when in fact 1 Maccabees says it was on the Brazen Altar.

I don't think it's a coincidence that the Baalbek Temple built by the same architect so closely resembles the basic lay out of The Temple Mount, with the Hexagonal Court being what become the Dome of The Rock and the Temple proper being the Al Aqsa Mosque.  Though the Southern Conjecture/Al-Kas fountain view proponents of whom I have been one in the past are perhaps assuming too much about the location of the Equestrian Statue being the same.

I'd like to see the primary sources on Byzantine Jerusalem's Church of Holy Wisdom discussed by someone without an agenda.  How true is it that it stood where the Dome of the Rock is now and that it was identified with a location relating to the trial(s) of Jesus?

Those who believe the Temple was where the Dome currently is say that spot was identified as such by Muslims right from the time of Umar.  For one the oldest Muslin worship site on the Mount is the Al Aqsa Mosque, the current silver domed building is slightly younger then the Dome of the Rock but it was still where Muslims prayed first.  And even then many scholars now think even that oldest primitive Al Aqsa Mousge doesn't go back to Umar but was founded by Muawiyah.

There is no real detailed contemporary account of what Umar did in Jerusalem.  The account typically used by Gihon Spring proponents is a 14th Century account.  Given my personal theories about the early history of Islam(that it was really just an Ishmaelite form of Christianity originally), I suspect Umar never intended any Mosque to be built in Jerusalem as he wanted it to remain a city for the previous People of The Book and if he prayed anywhere it was only the location just a little east of the Holy Sepulcher.  He captured the city because of his alliance with the Jews and Miaphysite Christians who'd been persecuted by Heraclius.  The Qurran does teach that the Land of Israel belongs to the Children of Israel.

Likewise when the Crusaders controlled Jerusalem they called the Al Aqsa Mosque the Temple of Solomon and the Dome of The Rock the Temple of The Lord, The Lord in Christianity is Jesus meaning that name implies a New testament significance.

I'm going to Copy/Paste from The Bordeaus Pilgram (333 AD) via this website.
http://andrewjacobs.org/translations/bordeaux.html

There are in Jerusalem two big pools to the side of the Temple, that is, one to the right, another to the left, which Solomon made, but inside the cite there are two twin pools with five porches, which are called Bethsaida.

There those who have been sick for many years have been healed.

These pools have water which becomes scarlet when disturbed.

There is a crypt there where Solomon tortured demons.

There is the corner of the highest tower, where the Lord went up and he said to the one who was tempting him, and the Lord said to him: Do not tempt the Lord your God, but him only should you serve (Matt 4:7, 10).

There is the cornerstone about which it was said: stone, which the builders reproved, this has been made the head stone (Matt 21:42).

And under the pinnacle of the tower there are many chambers, where Solomon had his palace.

There is also the chamber in which he sat and wrote about wisdom; but the chamber itself has a single stone for its roof.

There are also very great pools of water underground and a great pool built with work.

And in that building where the Temple was, which Solomon built, in the marble before the altar is the blood of Zechariah which you would say was shed today; indeed, there appear to be traces of the soldier's boots, who killed him, throughout the area, such that you would think they had been pressed in wax.

There are two status of Hadrian; not far from the statues is a pierced stone to the Jews comes every year and they anoint it and they lament with a groan and they tear their garments and then they withdraw.

There is the house of Hezekiah, King of Judah.

I have come to believe all of this section is about stuff on The Temple Mount.  After this he heads south out of what was then the city proper where he observed the Pool of Siloam then goes to the Western hill which was considered to be Zion at that time.

The use of the name "Bethsadia" is confusing because the New Testament and Josephus use that of a place not anywhere near Jerusalem.

There are at least two probably three different stones refereed to here. However people confident The Dome is the site of The Temple seem to treat all three as the same and as being the titular Rock under that Dome.  I have my doubts any of them really match that Rock but the best bet is that the modern "Well of Souls" is what this Pilgrim identified as the chamber where Solomon wrote "the book of Wisdom" (whether that is the apocryphal text or they meant Proverbs I won't venture to guess).  This association could explain why a Church built there later was called Holy Wisdom, but again I need an unbiased way to analyze the more obscure primary sources on that Church.

When the Pilgrim says "and in that building where" he's clearly moved to a more specific location and so the stone that will be mentioned last can't be identified with the two prior stones.  Those two stones are explicitly not in The Temple proper.

Identifying the Dome of The Rock as the Temple's Location depends on the "pierced stone" the Jews came to anoint every year (we know elsewhere that day was the 9th of Av, not Yom Kippur as one article I read criticizing Cornuke assumed).  This stone was (believed to be) either a Cornerstone of The Temple or one which was supposed to be where The Ark rested and so probably only slightly larger then The Ark itself, something more like the Stone around which The Church of the Seat of Mary was constructed.  But on second thought this Stone is not actually likely to be where the Holy of Holies was since The Jews have always been adamant about not risking accidentally walking over it.

So yes, I still consider the Dome itself the least likely of spots on The Mount to place The Temple.  I have become more open to the Dome of The Tablets view because that places it directly due west of the Golden Gate.  However the narrative thrust of the Pilgrim's description could be seen as moving southward and thus placing The Temple south of the presumed Chamber Solomon wrote the Book of Wisdom in.

I am far from making up my mind on this issue.  I'm still attracted to the Nea Church being the site of at least one of The Temples, or maybe David's Tabernacle.

Update: An article called The Byzantine Presence on The Temple Mount arguing for the Gihon Spring view is very misinformed and since fact checking it's claims I now doubt that Saint Sophia/Holy Wisdom was on the Temple Mount.

It once accuses a Wilson of wrongly conflating the Church of the Blessed Mary with the Nea Church of the Theotokos.  However it is in fact well known that both those names were used for the same Church.  Cyril of Scythoplis account of the Church's origin makes clear that Sabas's request was just of a Church for Saint Mary.  It was Justinian who took the prerogative of using the title Theotokos because of his agenda of trying to unify the Chalcedonian and Miaphysite churches while scapegoating the Nestorians.  Both this source and Procopius only refer to Justinian building one Marian Church, and none of this article's sources are aware of the Theotokos Church if they were indeed different.

The Saint Sophia Church is clearly near by and so I'm now thinking was maybe where the Armenian Church of the Archangels is with it's presumed trial location changing.  Carefully reading that article's own sources the "Stone" venerated here that Jesus stood on is clearly a smaller portable "stone" not something like what the Dome is built over.

I personally think the tradition of sealing off the East Gate began in the Byzantine era by Christians who felt it was time to fulfill Ezekiel 46:1 since Jesus had already entered at his Triumphal entry.