Your bath vent should have a lousy 12V fan in the vent...That problem solved.
Your bedroom vent IF it has any wiring AT the vent it will be 120VAC for an optional A/C unit. When I added my Max air to my bedroom, I just fished 12VDC to the nearest light. On my model the center ceiling light is NOT switched, so I have constant 12V for the vent. If yours is switched, you can always just turn the light off at the light.....problem solved again
As for the living area, I would do the same as the solution for the bedroom for the quickest and easiest install.
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2012 Copper Canyon 273FWRET being towed by a 1994 Ford F350 CC,LB,Dually diesel.
Airlift 5000 bags, Prodigy brake control, 5 gauges on the pillar.Used to tow a '97 Jayco 323RKS.
Now an RVIA registered tech. Retired from Law enforcement in 2008 after 25+ yrs.