I was composing a post similar to yours Joe but considered the system was connected to the coil + post therefore the possibility exists, however rare, that a problem could affect operation. A short to ground in the alarm system positive attached to the coil could stop the engine. I don't think that is what is happening here but eliminating it as a possibility takes it off the table in troubleshooting.
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Neil
1977 Catalina 30
San Pedro, California
prior boats 1987 Westsail 32, 1970 Catalina 22
Had my hands in a few others
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