When we take the plan of the temple and put it on the plan of Jerusalem with the building behind the temple placed on the old town of Jerusalem the altar (which is the location of the 3^rd temple) will be located on Mt Gibeah which nowadays belongs to Jerusalem. This is the only hill which fits in. It has a direct south- north axe to the old town of Jerusalem.

Test it out. If you place the Plan of the temple/ the Heave offering of the land on Jerusalem you can see that there are not many options. The centre, the place of the Altar is the place where the 3^rd temple is located. Isn’t mt. Gibeah the only logical place?
 
Isn’t it markable that this place is held free for many years? No other religion or King was able to occupy and build something on it (there is only the ruin of Kg Husseins unfinished palace).
It has actual room for the square of 500 cubits. It is the highest place in the region.
I think Mt. Gibeah is probably the new Zion.