1996 Chevy Silverado running lights and radio & A/C ind

I would check the bulbs. They do burn out after time. Yours is a 96, I have a 2000 and I had to replace 7 out of 10 of my radio back lights (burnt out) by disassembling the radio and solderig new bulbs into it because I couldn't read any of my radio control buttons at night. Most of the backlights in the dash are very tiny "Incadescent" bulbs that do burn out over time. I would say that your A/C light(s) issue is the same as the radio. As far as the running lights, if you mean the Day-time running lights (DRL), they are bulb #2057 and need replacing (my experience) about once a year.