#20 is a thrust bearing.----Reverse gear floats on #29.-----None of these items have anything to do with reverse gear shifting , unless there are parts missing. !----Are you prepared to do some simple inspection on this lower unit ??
No---Item #10 is the shift piston.----For reverse it needs more oil pressure to compress the spring.-----If someone fooled with solenoid adjustment that could also be an issue.---Clean the shift piston bore.---Replace o-ring item #8
The engine block will not fit on a motor of 1973 and newer.----Sounds like an issue with shift piston bore.----So clean the bore.----Test shift function before installing the lower unit on the motor.
???----On a 2 stroke the gas would still go out the exhaust to be wasted as well.----Not rocket science.----P;ease review your understanding of how a carbureted 2 stroke works !
Guessing gets expensive.----Do some tests on stator and trigger.----Also charge battery / load test battery and take starter apart for cleaning and ohm test.
You cannot safely run one of those motors with carburetor issues.----A plugged carburetor means you might be starving 2 cylinders of oil.----And it needs a new water pump impeller every 3 to 5 years.