hence the "probably"... Most are off/1/both/2 now. many years ago there were off/1/2/both or 1/off/2/both which are a problem. Never go to or thru OFF with a motor running.
Also, we don't know if his switch is broken...
I sounds, from the first post, that the 1 battery was 9 volts at some point. He was running on Both before that. I would suspect the Batt 1 is bad, not charging or holding a charge. This could be from constantly being draw down by the stereo or something else when they are not on the boat. Eventually, it won't charge back up. Sounds like they replaced a battery once. Is batt1 the new one? The dealer would have looked for bad connections and a bad switch but maybe they missed something
step 1a Pull the fuse to the stereo and listen to the water and the seagulls
Step1 b Always turn the switch to OFF before you leave the boat. that way anything you left on won't kill the battery.
Step 2 Pull Batt 1 out and have it tested.
Step 3 Run on batt2 and verify there is no problem
Step 4 put batt 2 in batt1 position, switch to 1 and see if there is a problem