Nearest I can figure/find out:
2502 = Horsepower/Generation
F = 1989 (model year)
10378 = Serial Number
For parts, call your local Yamaha Marine Dealer.
Bingo!
I had an older Honda in the shop with the very same symtoms.
Turned out the exhaust manifold had a hole burned through...Too bad the part was NLA and was not financially feasible to remove the powerhead.
Normally connected to the fuel pump with a see-through hose (NOT the fuel line).
This hose allows the skipper to view the condition of the fuel pump diaphram. If you see fuel in the hose, you have a ruptured diaphram.