International 4300 dt466 low voltage (dashboard)

I have a 2005 international 4300 dt466. Turned the truck on and on the dashboard, the red light next to the "volt" gauge came on. Volt shows low at 12. All the lights on the truck work fine and the truck will start. Cleaned around the battery. Any ideas on why it's low? How do I start trying to fix this? First thing I should do?

Since the lights work and it starts, I'm thinking the battery is good. Any ideas or could I be wrong?

Weather is at 48 degrees right now. Was at 38 yesterday night when I first found out about this problem.

 

Checked those connections and they are fine. Tested both batteries and one was a "bad battery". The other was low at 12.4v. After installing new batteries, the red light next to the volt gauge is no longer on but the volt reads 13v. When I turn the interior lights in the truck, it drops back down to 12v. Any ideas what else it could be?