The Torah tells us (Shemos 32:25 - כי פרעה אהרן) that Aharon was one of the kings of Egypt, a Pharaoh. When did he rule there, and is there any other evidence of his reign?

This question is Purim Torah and is not intended to be taken completely seriously. See the Purim Torah policy.

Indeed, Hilel tells us (Mishna, Avos chapter 1),

Be among the students of Aharon: loving peace and chasing peace

The B'er Hetev asks why he has to say both. Surely someone who loves peace will chase it. He answers that sometimes someone loves peace so much that he wants it to chase him. We see this by David who loved goodness and kindness and prayed (Ps. 23:6) "Only may goodness and kindness chase me"; the same is true for peace. But Aharon, he explains, was different. He not only loved peace but chose to chase it. How did Hilel know this? It says in B'shalach (Ex. 14:8) that the pharaoh took his best chariots and chased the Jews. It clearly wasn't to fight them: there's no mention of weapons in what the pharaoh took. So he must have been chasing peace. And we know this was Aharon because Aharon was not with the Jews until here (there's no mention of him from the exodus in 12:51 until this point) but he was after this point (he appears again a short while later in 16:6).

An anonymous friend of mine answers:

שמות רבה (וילנא) פרשת ויקהל פרשה מח

ד וכל...בית הכהונה ובית המלכות, יוכבד נטלה כהונה ומלכות אהרן

Yocheved inherited the priesthood and the kingship of Aaron. So Aaron was Yocheved's predecessor as Pharaoh.
If Aharon was Pharaoh before Yocheved, then he must have been Pharaoh in his youth while his mother was still alive.