I doubt you've owned this 30-YOA unit since new, so you don't know who's been tinkering, or what may have been ignored.
The Shore Tie Power and the Generator Power both wind up in the Panel, but they follow slightly different paths.
So YES, inspect Transfer Switch and its connections. Actually surprised a 1988 Class C even has one. With many that age, "transfer" happened by plugging the Shore Tie Cable into a Pedestal-Type receptacle powered by the Generator. So your TS may have been a modification, and quality of installation becomes suspect.
Uncover your Panel and tighten every terminal screw.
Often, the flexible Shore Tie Cable is spliced into "hard wire" where it enters the coach. Find that box, or whatever it is that connects Shore to Coach, and make sure those connections are good.
