[villagetinker]

Electric carts have some interesting wiring. I am GUESSING, but I think there may be a wiring problem with the 12 accessory socket you are using. Have you tried say a 12 volt trouble lamp, or some other 12 volt device to see if the same thing happens? If so, i would very carefully check (or test) all of the wiring associated with the 12 volt tap. I did some work on a couple of 36 and 48 volt golf carts, and found the wiring to be very confusing, especially with regard to "ground" connections. Also, did the 12 volt tap work before, did that phone charger work before?
Back to your question about your batteries, they sound like they are in very good condition, I think you have a problem with the 12 volt tap that is somehow effecting the electronic controls of the cart. If you can get an accurate wiring diagram for your cart, I would be willing to help you trouble shoot if you are interested. Send me a PM.