Had the prob with my own 1986 Bayliner Capri which has an OMC 3. 0 liter also. Was really lucky someone suggested checking the bellows when replacing that cable cuz one of them had gone bad so I did the whole thing at once. Check em just in case.
Well since someone gave the most common answer for this problem I'll try to help with info on replacing. It isn't too difficult. Disconnect the lower shift cable at the engine where the connections, remove the other end of cable at transom plate on outside of the boat.
When a lower shift cable starts to go bad it doesn't slide as easily as it should which results in stalling when the boater attempts to put it into the neutral gear. The cable sticks which causes the shift interrupter to not work well. Replacing the cable should work.