I sort of covered Gordon’s Calvary in a former thread (way before the forum revamp):
Will the Real (Insert Place Here) Please Stand Up? - #16 by patrick457
In a nutshell: ever since the 17th-18th century there have been people have begun to express their dissatisfaction with the traditional site, first and foremost because it is now currently
within the city walls - whereas it is clear from the gospels that Golgotha was
outside the city. It happened that most of these people were Protestants who did not have any territorial claims at the Church of the Holy Sepulchre and who felt that the traditional site is too cluttered.
In 1841 Dr. Edward Robinson’s
Biblical Researches in Palestine, which at the time was considered to be the standard work on the topography and archaeology of the Holy Land, argued against the the traditional location (p. 407-418). He believed that the traditional location would have been within the city walls also during the Herodian era (something modern scholars now dispute), and he argues that the tradition surrounding the Church of the Holy Sepulchre isn’t as authentic or as reliable upon closer scrutiny as supporters would have them. He was careful not to name any specific alternate candidate; he did, however, suggest that the crucifixion would have taken place “upon the western or northern sides of the city, on the roads leading towards Joppa or Damascus.”
Motivated by Robinson’s research, a German author named Otto Thenius proposed that a rocky knoll north of Damascus Gate, which, as Thenius noticed, resembled a skull, was the biblical Golgotha. Thenius’ identification of the skull-looking knoll as the biblical Golgotha became popular and was repeated by a number of people, but it wasn’t until the famous Major-General Charles Gordon expressed his support for this location - based on a rather peculiar (okay, to be blunt, ‘weird’) kind of typological/mystical reading of the Bible - that the site received major attention. And that’s why the area is known as ‘Gordon’s Calvary’ today.
And here’s the thing. Gordon’s claims gained fame and publicity, not so much for any scientific validity but because of Gordon’s compelling personality, his heroically tragic death, and his fame in contemporary British society. In other words, the site became popular because Gordon was a popular guy, so everything he says must be true.

Critics would say that the weakness of Gordon’s theory is precisely because Gordon seemed to be over-reliant on his emotions (he didn’t feel anything special about the Church of the Holy Sepulchre, but when he encounters this site he’s like “I
feel this is the real place”) and personal interpretations of Scripture rather than any solid research.