Do you have to be in your reserve unit for a certain amount of time before switching units?

It will depend on the Commander. You can submit a request to transfer, but that doesn't mean they will sign approval for the transfer request.

Gaining commanders no longer need to sign 4651R for TPU transfers as of 2years ago. For promotions, need to stay min 1 year.

Not exactly, but your contract may have membership stipulations.