Thank you for the numbers so I can check the wiring
Down side is BB used a suppliers wiring diagram which is less than useless as it does not show what any plug attaches to and is pretty well unreadable to boot.
So will will have to treat this as a Russian made mower with instructions written in Galic translated by Kenyan .
With a meter or test lamp check the seat switch , parking brake switch & lap bar switches
And these are easy because you just check for battery voltage at the plugs on the back of the switches in start mode .
These switches should be closed when the plungers are depressed
This is handy because each switch can by bypassed one at a time with a short jumper wire with a male spade ( blade to some ) terminal on each end .
The USUAL wiring is key => pto => parking brake => lap bars => starter solenoid and that is what the Elite doe . but it has 5 relays
However your mower is shown as having 4 relays
One of these will be the starter relay and send 12 V to the starter solenoid
With a bit of luck, it will have the same colour wire as the wire at the base of your solenoid
As it uses a relay, then the switches on the lap bars could switch GROUND to the starting relay while the key switches power to the starting relay
So you will have to work out which relay does what
take the cover off and listen / feel them
One will trip as soon as the key is turned on and will stay tripped in both the on & start positions of the key
This is the ignition relay if the switched terminals are 12 V or the magneto relay is the switched terminals are ground ( grounds out the magneto )
Another one will trip when you lift your bum off the seat and the key is on, that is the seat relay
The other two should be the lap bar relays & PTO relay
How they are wired up is any bodies guess as BAd Boy wiring seems to be designed by boilermakers who are colour blind .
Has it ever run and this problem just happened or did you buy a "mower with attitude" in the hope you could re-educate it ?
Most control modules switch the grounds and if you have had a bad ground connection this may have blown the module