Using house battery graduall discharges chassis battery?

Disconnect one battery's wire from solenoid. If both batteries keep marching in lockstep the solenoid will have been eliminate as a suspect. I assssssume you did check for the presence or no of voltage to one of the solenoid coil terminals?

Also, a charge solenoid power studs should have only TWO battery wires connected to it - not three or thirteen. If you have more than two wires connected to the vig studs, someone screwed up. One oe more wires is fitted to the wrong stus.