So far so good. I ran the cart for a couple hours tonight pushing 2 amps and 6 speakers on top of the led lights. The auxiliary battery never seemed to lose any power. The reducer is hooked up to a switch so I can turn it on and off. We set it up on the same switch that turns the audio system on so it would feed the auxiliary battery while in use.
I guess that I could leave the switch on and radio off to charge the auxiliary battery while charging my cart. I'm going to run it this way for awhile and see what happens.