Get a paint stirring stick and break off a couple inch piece and then the next time it doesn't engage, balance the stick on top of the switch on the starter (round button). If the spacer shim cures the problem it's likely worn linkage and if not it's most likely the starter switch. We used to use a book of matches, folded cardboard, and once my billfold (it was always skinny back then) for an emergency start situation.
