How long does a person wait to be an R4 again, when they rejoin the group?

The ranks and positions in an alliance are given, and taken, by the leaders (R4 / R5). They can be changed at any time. If you want a higher rank then it is up to the leaders to give it to you.

New members would need to demonstrate that they are active and worth being one of the R4 leaders. If you were one before then you could just ask for your position back.