FWIW
My phantom electrical problem kit is a bag of jumper wires with male terminals at each end
The proceedure , in your case is to use these to hot wire every switch starting with the key switch
Because you have an interlock module yours is a bit harder because you need 1 double lead so you can connect B to S and A to power the module
When the problem is found, the engine will spin so that makes it a bit easier .
If jumping all of the switches does not work then check the module is getting the power / ground that is should be according to the switches by back probing the module plug.
IF yes then the module is bad if no then there is a bad connection between a switch & the module
Mowers are cheap so the crimped on terminals have no support and are prone to fracture at the crimp
So if the mower works perfectly with the switches jumped hold the plugs and wiggle the wires to see if one is bad .
Naturally you will need to work through the wiring diagram to work out which should be open & which should be closed .
Takes a lot of time , removal of hair by clenched fists and making holes in brick walls with ones forehead but if you are methodical you should be able to get through it in a day .