Yes the sol. is piggybacked onto the starter. Swap batteries, good advice. The fact that your alt is only putting out 13 volts is a problem. It should be more like 14 or 14.5 Was this measured with a meter or the dash gauge?

A gun in the hand is better than a cop on the phone.

98 Passport 33's, Supercharged, Calmini Bumper, rockbars, diff drops, Teralows, 4.77's, Aussie and ARB lockers, Safari snorkel, Optima red top.