2004 peterbilt voltage drop

I have a 2004 Pete with a C-15 in it. Whenever I turn on my headlights, clearance lights, and my blower my voltage drops down to around 13 which I feel is plenty. But it will start beeping at me sometimes. It’s not all the time and it will beep and then kill my tach, Speedo, water temp gauges. It has a red square low batt on the dash it doesn’t flash or anything. It only does it once it gets around 12.8 or 13 volts with everything on. That’s what makes me think it some kind of safety. Any help would be great. Thank you

 

I will test voltage out of alternator again but last time I checked it was fine but will double check it. thank you

as for the accessory relay I assume your talking about the panel down by the clutch? Thank you also appreciate your guys help for some where to look

 

Okay I will check that. It doesn’t effect my lights. Just my gauges, blower motor, wipers. Lights might be wired different.

 

Thank you everyone for the help. I ended up testing voltage out of alternator and I couldn’t get it to ground from the ground wire. The bolt for the ground was just barely holding on went to take it off it literally just broke. Drilled it out and retapped it and everything has been good the last 2 days! Volts are staying up now