Hey Tom, we have a 361 too and started having the same problem a few years ago and it seems to be affecting cockpit panels in counter clockwise direction starting with swim step and port side.
I tried quite a few repairs and none of them worked for more than a season and each time made it look worse with goop under the teak so I opted for replacement. I got the new panels from Beneteau, they were available on their parts site. Delivery was a couple of weeks and first round I just got one panel, second round I got one of each so I still have starboard seats in garage ready.
Replacing them is actually not that bad, just rip it off, use a scraper to get the glue and pieces left on the seats off. Get a good teak glue, I got one in plastic tubs but can't remember what its called but I'll look for the bucket when I get a chance, they had great support too. I drilled small holes in the black joins and used small screws with big washers to put pressure until the glue hardened, dipping the screws in lanoline so not to get blued in. The glue company also had the black caulking so taped around and applied caulk. I put the first panel in 5 years ago and its still holding up.
Personally I wouldn't bother with repair but go right to replacement, squeezing glue under or trying to clean it up won't make a good bond and it'll leak again. I also got all panels due to the time it took to get it, if I remember right they were $150ish each.