Question: My cousin waited too long to get his permit. Now there is no time before the election for him to do NRA training and get a permit using that. Is it legal for him to buy a pistol from a gun show without a permit?
Yes, but he won't be able to walk out with it either. Depending on the locality, he'll have to wait the required time to take possession.
You still have to fill out a yellow sheet at gun shows if you're buying from a licensed dealer.
Private sales on the other hand...
Depends entirely on the state.
Remember: the next prez isn’t sworn in until January 20, and can’t enact infringements instantly. Tell your cousin to start the process NOW - yes, there is still time. Just do it already.