I appreciate all these responses! Much of it is over my head, but I will print this out for when I have the electrician out.
I had unplugged everything in the garage (except the garage door openers) to try to eliminate any noise, so I don't think it's a load problem.
At work we just replaced two of our fleet vehicles with EV's and our electrician is preparing to get level 2 chargers installed for these and for employee vehicles. EV charging is new to him, and he is wanting to learn everything he can. He's very interested in my problem and has offered to come out and take a look. I think I will first see if I can borrow one of the EVSEs from the fleet vehicles and see how that behaves in my garage to rule out the EVSE. If that shows a fault as well, I'll have the electrician come out and hopefully be able to fix things without too much trouble.