Hey DougM,I have a similar issue with a 2GM20F. It starts fine at the dock,but after being out sailing for awhile with the electronics powered up, I push the starter button and get nothing.
Sometimes bumping it a couple of additional times, the engine will crank rapidly and start immediately.. If that doesn't work, switching to the second battery does. I know that it might be the contacts in the start button, and I have seen other threads indicating that it might be a wire size issue in the starter circuit.. I believe it's the white wire (somebody else may be able to verify that). I believe some have wired a relay into the circuit as well.