It appears a key innovator in this theory was Dr. Ernest L. Martin's 280-page book entitled Secrets of Golgotha. It can be found on Amazon, but not currently for a reasonable price.
Bob Cornuke wants to argue for it as if it specifically proves or is dependent on his model for The Temple's location. It's not, the issue of the traditional sites being north rather then East of the Temple is the same with all four proposed locations for The Temple. And the Mount of Olives is actually far enough north to arguably fit a Temple Mount location better then Cornuke's. I still favor the Al-Kas Fountain view.
John 19:21 tells us the place where Jesus was buried was right by the place He was Crucified. We also know this Tomb was originally the tomb Joseph of Arimathea had prepared for himself. Arimathea is probably a Rama or Ramath of the Hebrew Bible. Joshua 18:25 and Nehemiah 11:33 places one in the territory of Benjamin, and Judges 19:13 and Isaiah 10:29 seems to place it near Gibea. Though Judges 4:5 places one near Bethel. Why would he have a Tomb near Jerusalem? Well let's get into that.
Zechariah 14:4-5 has lead many Jews to conclude that The Resurrection of The Dead will begin at the Mount of Olives. I'm not sure why that is, I don't see the Resurrection in that verse. But because of this many Jews have wanted to be buried on the Mount of Olives. (Mount of Olives description, from www.goisrael.com, retrieved January 4, 2012.) And it seems this tendency dates back to before the Time of Christ. So that makes the Mount of Olives the most likely place for someone like Joseph of Arimathea to have a Tomb built.
I've also been exploring on this blog the idea that most of Zechariah 12-14 was fulfilled from 30-70 AD. What if the Earthquake caused by The Messiah standing on the Mont of Olives is either the Earthquake associated with the Death of Jesus, or the one that rolled the Stone away at His Resurrection?
That would mean the Resurrection did begin there, first with Jesus but then also as Matthew 27:51-53 says many others who's tombs were split open by that Earthquake soon after. Which I feel ties into Daniel 12, the only other passage on the Resurrection that says "many" rather then all.
The Biblical designation "Mount of Corruption", or in Hebrew Har HaMashchit (I Kings 11:7–8), derives from the idol worship there, begun by King Solomon building altars to the gods of his Moabite and Ammonite wives on the southern peak, "on the mountain which is before (east of) Jerusalem" (1 Kings 11:7), just outside the limits of the holy city. This site was known for idol worship throughout the First Temple period, until king of Judah, Josiah, finally destroyed "the high places that were before Jerusalem, to the right of Har HaMashchit..."(II Kings 23:13)
Ezekiel 11:23 says "And the glory of Yahuah went up from the midst of the city, and stood upon the mountain which is on the east side of the city.". That would be the Mount of Olives.
Zechariah compares this Earthquake to the Earthquake in the days of Uzziah. That Earthquake according to Josephus Antiquities IX 10:4 ( about 2 Chronicles 26) also involved the Temple being rent. Meanwhile, there is archeological evidence Uzziah's body might have wound up among those buried on the Mount of Olives, the Uzziah Tablet.
In 1931 an archeological find, now known as the Uzziah Tablet, was discovered by Professor E.L. Sukenik of the Hebrew University of Jerusalem. He came across the artifact in a Russian convent collection from the Mount of Olives. The origin of the tablet previous to this remains unknown and was not documented by the convent. The inscription on the tablet is written in an Aramaic dialect very similar to Biblical Aramaic. According to its script, it is dated to around AD 30-70, around 700 years after the supposed death of Uzziah of 2 Kings and 2 Chronicles. Nevertheless, the inscription is translated, "Hither were brought the bones of Uzziah, king of Judah. Not to be opened." It is open to debate whether this tablet really was part of the tomb of King Uzziah or simply a later creation. It may be that there was a later reburial of Uzziah here during the Second Temple Period.And if you think Uzziah's action sounds like a good type of the Antichrist or the False Prophet. Well Daniel 12 implies this Resurrection will include some who wind up in the Lake of Fire also.
Update October 22nd 2017: I may abandon this.
Mark 15:37-39 is the key to the Mount of Olives view. I get why it seems to many to say the Centurion (who's probably not the same soldier who pierced him in John 19) must have seen the Veil being torn, putting them to the East of The Temple. However verse 39 is pretty specific that Jesus crying out and giving up the Ghost is what the Centurion saw to cause this reaction. The fact that he died at that exact moment by his own will is what impressed this Roman Solider, who was probably raised to value controlling one's own death. He wouldn't have cared about a decoration in the Jewish Temple.
And with that smoking gun weakened, and my dependence on extra-Biblical sources here. And that the NT does clearly refer to the Mount of Olives in other places. Has caused me to come to doubt this view now.
As far as Hebrews 13:11-12 and it's comparison to Jesus Crucifixion as where the "Without the camp" reference. They are forgetting Exodus 33:7 says the Tabernacle as without the Camp. I don't think the intend of this verse is to be a clue to the geography of Jesus Crucifixion.