SCBillandJane,
The battery was toast when I bought by 2003 last year, so that might be your case, also. That was the 1st thing I had to replace.
The running lites and brake lites use your tow vehicle's electricity to power those.
I would think that a 15 amp receptacle should power the converter only, but hopefully others will chime in if that is not the case. I do that with no problem, but when I did the initial check on my AC using a standard recepticle to see if it would work, I fried the adapter
.......but the AC pulls a lot of amps.
I wondered about that little thing with the red lite on the back of the front shell also. And yes, that is the radio antenae.
Chap