TNCharlie

I need some suggestions. I recently got my hands on a sweet 65 with a great body and new interior but a tire motor. When I was taking my wife for a ride last week, I realized the driver side motor mount was broken. I found this out when I took off from a light (not in a racing way but I was not ***** footing it) and the throttle stuck. I notice the transmission selector move to the right. I took it staright home but noticed the ALT light lit. AFter some trouble shooting, I found the battery is at 12 V with the engione off and about 13.4V when it is running. This tells me the alternator is working but the damn light is still lit. The connections to the alternator are good. Is there something I am missing?