If you are metering battery voltage after the battery , on the HOT side and it drops to 2 or 3 volts, shouldn't it read zero if there was a break in the HOT side somewhere ? Being that there is a partial voltage reading ,
Why Not also look at the negative side ? Could this be ground related ?
Could it be a broken ground wire, caused by someone poking a pointed test probe through the wiring covering in the past to test the circuit while doing some kind of installation.
The hole in the insulation has allowed moisture to enter the wire inside, creating corrosion and maybe causing that wire to fail or partially fail ?