It would help to know the year and model.
The light may be on because the boost switch is stuck or broken.
The switch controls an interconnect solenoid. The only time you should get the light is when the switch is on, it is spring loaded to return to off.
The interconnect solenoid connects the chassis and coach batteries together. It should operate automatically and connect the batteries together when either the coach or chassis batteries are charging so all will charge. You don't get the boost light during auto operation. It auto opens after a while when charging stops.
If your booster switch is stuck or broken and the solenoid is actually energized it will drain all batteries in a few days because the solenoid draws a couple of amps.
On mine there is a 1 amp fuse on the DC fuse panel for the solenoid.
Most RV batteries live a long and useful life, some are murdered.
2000 National Sea Breeze F53
1998 CRV Toad