That switch setup is pretty easy to wire. ANY, ALL, and EVERY B+ (battery positive) feed/out, needs to connect to the common post of the switch. This insures that all electrical device work whether the switch is in ! 2 or BOTH. This also has all loads off when switch is off. The only exception, is the auto-bilge brown/red wire. It should go directly to the battery B+ post. So at the battery, you should only have one main cable connecting the battery positive/B+ post to the switch posts "1" and "2". Helm BUSS, alternator/starter, stereo , etc, all go to the "C" post of the switch. Only the auto bilge connects directly to the battery.
One battery should have the boats main GND cable connected to it and then there will be another GND cable connecting the 2 batteries. All ground cables need to be split between the 2 batteries, so no single ground post is stacked with too many.
You will probably need a volt meter to help diagnose the issue, but also physically tracing these cable down is the best place to start. Knowing where the cable comes from and where is needs to go is the beginning. Once that right, the meter can help to diagnose/test the system electrically.
The volt meter will also help you diagnose the bilge pump issue. Is it is an auto bilge with an internal float switch or external float?
If the stereo powers up with the key in the "RUN" position, then it should still power up when in the "ACC" position. If this is not the case, then the switch would be the fault. the "ACC" terminal should be hot in both "RUN and "ACC" positions. Here again, the volt meter will help you test whats going on with the yellow and red wires at the head-unit.