Along with what Mike wrote above,

A boat will often start with only 10 volts. Solid state electronics and lighting can be more voltage sensitive.

I wonder if the alternator/starter feed is connected to a different battery than the other electronics as you have it wired currently or as you have things selected. Circumventing the battery switch and going battery-direct on some accessories could be problematic. There could be a difference in terminations, grounds or recharging of the two batteries.

Take just one circuit off line at a time and test. If one of these problem circuits has an inadequate ground or a moderate short, it can siphon voltage from the other DC circuits in parallel causing a voltage drop. Also, a B+ supply, with a number of low resistance DC bulbs in parallel can measure like a ground, especially with a test light, while that particular circuit is off. So check each assumed ground for what it shouldn’t be (DC voltage) before confirming what it should be. Don’t forget to turn a dash light dimmer rheostat to full before testing.