Welcome to the board! That's one of the cleaner vintage Supras I've ever seen. It looks like a survivor -- all original teak and it looks realllllly well taken care of. Congrats!
The leak is probably the rudder seals or the prop-shaft packing. Your exhaust is probably also leaking. I'd address all of these just as regular maintenance. These old boats all leak a little bit, you just want to limit how much.
Also -- check your stringers. This one looks well taken care of but that doesn't mean the stringers are good. Search the forum and you'll find lots of info. If you do have a 1986 with original (and solid) stringers.... you just won the lottery!
Former owner of a 1987 Supra Saltare. Current owner of a Malibu 23LSV.