The kill tether that attaches to the switch, is a mechanical kill. When installed and engine running, if pulled it turns key to off. Engine will start and run and kill if not installed. Sounds like switch is working as designed.
That motor has been apart before...#2 has a Siezco piston, #4 looks to have a .030 piston(P3 casting) and had the new style head gaskets instead of original brown gasket. IMO I would just find a running motor and swap and use this one for parts.
A reman powerhead with warranty is $3K if you do labor for swapping. What you gotta figure out is what caused original to fail as you could transfer problem over to replacement and have it fail again.
