Voltage measurements depend on where you are measuring ...should be from Line to neutral initially and from other points through the circuit to the neutral.
Check, that is what I did - I had line voltage (120vac) on the wire marked RD which confirmed that the Pull/Push was making contact and had continuity. This is the source of the potential to ground and measured 120vac to neutral (which in this case is the ground center conductor of a three prong 240vac plug).
Therein lies a problem that only experience or knowledge of exactly what the flow process is in the machine operation can overcome.
This is caused by the fact that there is a mass of neutral switching that could throw you off course and make you believe there is a problem when there isn't.
As an example, assessment of the reading on 8 seems right (fault condition) but reading on 9 cannot be as it is switched neutral.
Other than that, your finding with the check switch is viable.
Always difficult to say from a distance as there are a lot of variables that affect the outcome.
I am not sure that I follow the logic on that since 8 and 9 are both hot (120vac) - The path starts at Line through the push/pull, through the lid switch, through the check switch, through the overload protector, they are tied together in the schematic in the motor (which works so the overload is good). I tested continuity from the ground plug to the wire marked GY at the top of the schematic and found it to be good - thus the neutral return through the switch was good (at least wherever the switch was rotated to). When I found that I had 120vac on orange 12, I knew the lid switch was good, the fact that BK M(8) and 9 had only 28vac confirmed in my mind that the switch was bad, jumpering from orange 12 to 8 made the machine start and the switched failed continuity test and had very high resistance. I thought that was pretty definitive. I hope you are not jinxing me now!