The idea of a pyramid on top the tomb was most likely copied from the pyramids of Egypt
Based on what little I know or can come up with, I agree.
By the way, Jewish tradition (Kohelet Rabbah) links "Zechariah's Tomb" not to the post-exile prophet of the Book of Zechariah but to Zechariah the son of Yehoyada', who was murdered during the reign of Judean King Yo'ash (2 Chronicles 24). On the other hand, local Palestinian Arab tradition calls the monument "Pharaoh's Wife."
Technically, "Zechariah's Tomb" is a nefesh, a monument built near, beside, or over a tomb. Several other structures or n'fashot topped with square or conical pyramids were found around/in Second Temple period Jerusalem: the "Tombs of the Kings," "Absalom's Pillar," and perhaps the Tomb of David. I was told that the First Temple era "Tomb of Pharaoh's Daughter" farther down the Kidron Valley just north of Silwan Village originally was topped with a square pyramid, too.
Thank you for allowing me to ramble and remind myself of what I used to know, or would like to think I used to know...
Sources: this one , that one , Zev Vilnay's Legends of Jerusalem, and old issues of Ariel and Kardom.