[Chip Chester]

If the machine is put together enough to run, maybe try this:

For the record tab, get a cassette whose content you can record over, but with the record tab removed, and make up a plastic shim and attach it to the non-sticky side of a post-it note. Place it over the record tab location with the sticky side of the post-it, and use a string or piece of tape to pull it away while recording is underway. See if it just stops, stops and ejects, or just drops out of record.
It could be that the switch mechanism is worn just enough that the slight extra thickness on the record tab 'cures' it. In that case, a shim or spacer at the right place in that mechanism (not on the cassette itself) could make it all better for the next 25 years.

Also, don't overlook a tensioning issue. If the tape path loses tension, the next thing I would have the deck do, if I were the designer, would be to have it eject because that would protect the tape the quickest -- get it unlaced, away from the spinning head (which would eat an un-tensioned tape) and back safely in the cassette.

Good luck! Just be systematic about your testing, and you'll get to the true cause.

Chip