Yes, EV's cooling fans run now and then when charging.My 2014 would do what you're describing. If I was in the truck when it did the weird needle dance it was very weird and a bit unnerving. In the engine bay there was always a series of electrical hums and clicks for several minutes after shutdown - people always thought the truck was haunted or something.
My 2021 ED doesn't have the same clicks and needle jumps but there are still sounds under the hood that I'm getting used to. I wonder if EV's have similar noises...?
Bob