12 volts seems low to begin with. mine is on 14 un less I put everything on, then it drops but never below 13 volts. is your volt meter needle constantly shaking back & forth ? batteries need to be checked. alt could also have a short too. it needs to be checked. battery testers can be bought at harbor freight for 20-25.00.
all cables connecting battery to battery should be looked at carefully. also & especially the positive cable to the starter along with the ground cable. a lot of these cables will corrode from the inside & you wont even see it from the protective coating outside. if jumper cables (the ones from batery to battery) are stiff, they need replacing. I replaced mine not long ago due to a short. the long pos cable cost me $20.00 to be made up. it was corroded real bad under the coating, but by looing at the outside it looked fine. I am not a mechanic but have diagnosed & fixed lots of things on my truck. I hope this helps you.. keep us posted.. good luck.