Oh but they do, Dan
Don't konw about your boat, but my '84 31' has the same problem, no juice to the steaming light. And, I know first hand that the only connection is inside the mast on the mast step. Looks like I too will have to pull the mast to check the connection.What's more, I just pulled the mast last winter, replaced everything and tested it all, everything was fine. My marina stepped the mast without me and voila, there's no steaming light! I am considering cutting an access panel to the base of the mast, a 3-4" hole to see if I can check it out. Several postings here have referenced cutting an inspection plate.Yes, this is/was ridiculous that anyone would engineer something in this manner.Good luck.