Update for future readers who may search and find this series of posts on the subject of solenoid "failure"...after installing the pull cord and running for a few days I would naturally instinctively continue to try the "STOP" button at engine
shut down. After several days of fairly calm sea conditions (read little bilge
spray or slosh) the Stop button began to work again like a charm. Not intermittently but flawlessly. The biggest advantage of the answers in the forum was that really no one had heard of such a failure and that led me to believe that what I was experiencing was NOT what the mechanic
had claimed but something else. So bottom line is that the problem I had experienced is clearly related to some sort of ground fault issue as Capngeo suggested.
Hats off to everyone for their help.