the gen lights usually indicate a low voltage problem.
your situation sounds funky to me I bet you have a few bad wires in your harness someware that are messing with eachother.
thats why I hate lights I like to see the voltage see the temp see the oil pressure
Main rig-1978 chevy 3/4 f/t 4x4 8" lift 38 14.5 16 toyo m/t's. BUILT 350(soon to be 6.2) quad batteries. front and rear 15k winches. lockers F/R. dana60 front full float corp 14 rear. th400/np203.
donor rig. 1988 GMC K3500 140k miles, th400. IFS(read CRAP) semi float 14 rear. drove it 142 miles home at 17mpg and 1/4 quart of delo 400.