Ok the green lanyard is so you can open and remove the dispenser drawer and manually unlock the door.
The other end just goes into the cavity behind /beside the dispenser drawer.
This has nothing to do with electricity.
Is is just more or less the same as weed eater cord.
And I have wondered for years why Maytag used a wax motor here also.
No other manufacture does they all use solenoids .
The length of the belt will not have anything to do with the unit pumping out!
If the unit is not pumping out and you have tested the pump with external voltage and the pump runs you have to be looking at a timer issue.
If your not getting water into the fabric softener it is also either a timer issue or the fabric softener dispenser is clogged.
If the belt is tight and not slipping on either the drum pulley or the motor pulley it is fine, no matter the measurement .
And yes from the wiring diagram the wax motor is 120 volt so yes you can test it.