The shaft the clutch gear slides out on May be binding Holding the Jack shaft out and that keeps the Juice to the starter motor... Freeing and returning after start.
Sticking is very common in old age.. Just ask us old-timmers. Eh
Remedy for me would be to take off the primary and have a look.. THEN.......
Remember,,,,,, When apart the jackshaft Doesn't have End support while the primary is off... Take plugs out to kick-over..No stress on this unit until the primary is back on...
The warning # 1 thing to do;;; is Remove the Battery ground wire FIRST ..
If the starter gear is moved on the jackshaft with battery connected it can take off the fingers,,,, Ask 3 fingered jack, He knows all about it...
signed....BUBBIE