I had the same problem once. When I moved the lower (outdrive) cable stud to the bottom of the shift plate lever slot, all better. If you're already at the bottom of the slot, Mr. achris's remedy above is your next step. He is referring to the lower/outdrive cable if you didn't know. What is the year and model of your stern drive?
Lower shift cable test
Remove lower shift cable from arm.
Apply grease to thumb and forefinger
Grasp black plastic sleeve and shift from F to R
If finger slips from black sleeve ,replace lower shift cable
To answer your question to me, my problem was shifting out of gear. That is when the 'Y' plate reacts to the dog clutch resistance on the lower cable and tweaks the cutout switch. The dog clutch is self engaging and only needs a little cable push/pull to bite. I'm going with the flow on this one. It sounds like your 29 yr. old lower cable is spent.