Basically the brake controller module is the interlock module too.
The brake control module is the ground source. I have several these mower with corroded terminals in the so call weather proof connector. I even seen pins of the modules corroded off. To test the module output ground turn keyswitch to run, be on the seat, and then see if the PTO clutch will cycle.
The brake module also control the 12v for key switch therefore controls the starter solenoid (relay). Most likely the harness and brake module has to be replaced. Unless you the tools, terminals, and connector to replace the bad connector but you still would still need a new brake module.
View attachment 69156