Good thoughts posted thus far.....

My $0.02....with even an inexpensive DMM/DVM.....start at the "common buss" on/near the panel with all batteries fully charged.
Measure D.C. Voltage at the buss main input with a battery connected....
Switch things on, read voltage....write it down....
Key mic and do other load things...record voltage under load.
Repeat with the other battery.....
If the large battery shows a bigger voltage drop.....work through connections back towards battery with same test....see where the voltage drops lessens....in between good vs. bad/poor voltage drop is likely a poor or bad connection.

Could be a bad crimp, poor solder joint, loose/poor screw connection, maybe even small wire gage (although not likely unless waaayyyyy tiny...).