I had the same issue where I was getting water in from the sunglass compartment. I never thought to connect to two issues. I have since unclogged the drain spouts. I have looked at everything and spent way too much time looking into how to fix. I was trying to avoid replacing the body module because I saw the price of the new module and was trying to avoid it. I opened it up yesterday and didn't see any stand-out issues like your photos but I am sure that doesn't mean anything.
Your dome light issue might be related to the door jamb switch being old? I just swapped one out. Pretty cheap and really easy to replace.
Toyota 4Runner Switch, Courtesy Lamp
Part Number: 84231-60070
Anyway, I greatly appreciate the response. This gave me the final push to just replace the damn body control module.
Last questions... Did you have to get this new MPX Body computer programmed?