OK Bou
Went through the 7000 series MTD manual which is free download from MTD ( mine came from the K & M site )
All the MTD's use the same wiring which is good cause you don't have to work through 20 variations of the same thing.
Looks like you do have a dodgey reverse switch.
IT is a crappy exposed blade on the FNR shift lever so would be prone to shorting out.
I never bothered to try & teach Granny to suck eggs so I ain't going to try & tell a competent tech how to test a mower.
It is all in the manual with lots of pretty pictures, and in colour to boot