INVERTER ISSUES! UGH! PLEASE HELP!

Do you leave the truck off the entire time you're using the inverter?

To prevent corrosion on the terminals/cables use battery terminal grease

 

Did you read the owner's manual for the inverter? Unfortunately that beeping could mean anything.

 

Without knowing the specs on your inverter it's not possible to precisely diagnose the problem. If you leave the inverter on 24-7 it's tapping your battery bank 24-7. Which is unnecessary and unadvisable. If the inverter is reading the voltage being low while no load on the 120ac it's likely your battery bank is weak. It might be just 1 crap battery. Even 1 crap cell in 1 battery. But the weakest link is the best your 12v supply will do. Swapping out 1 or 2 batteries will reconfigure the bank but now your New batteries are limited by the crappiest of the Old batteries remaining.
Your available 12v system is probably at around 14.4v while being charged via alternator. At 12v when truck is off. A few minutes of heavy loading on the inverter and it's down to 11 or 10v and every minute in that state is killing HOURS of life off the cells in the battery. (Actually it's # of charging cycles and depth of charging but nevermind all that lol...) It's damage is irreversible.
Bite the bullet, buy a whole new set of Dual Purpose (deep cycle and CCA) batteries for the truck. Turn off the 120ac side All Day Every Day unless you're using it and when you do use it run the truck.
Or put a harbor freight 2000w generator on the catwalk.

 

What size wires are they.
How long are the wires from the batteries to the inverter.
Are the red and black wires at opposite corners of the battery lineup.

 

Ground wire

 

Start with 4 new batteries. They do t need to be deep cycle, just get the big ones (950-1000CCA). Make sure your wires are at least 0 gauge and as short as is feasible.

I can leave my truck off all night and still make 12c of coffee in the morning w/o cranking up the truck. That's with the apartment size refrigerator running all night.

 

Gonna say 2 things. It's drawing too much current. So the wires are too small. Also batteries are prolly bad. Batteries in trucks don't last long at all. If you run an Inverter, you get about a year out of your batteries. Load test them and find out.