Hello Colton,
If you are not going to use this as a mower, all you need to do is run a direct wire from the 'S' (Starter) terminal on the ignition switch to the small 'hot' (ungrounded) spade terminal on the starter solenoid. This completely bypasses all the interlock switches that were in the circuit, as they are all in line with the ignition-switch-to-starter-solenoid wire. This is what prevents the starter from operating if all the safety switches are not in their proper position. Your schematic/diagram shows this as the White wire. Running a direct wire is much easier than trying to join individual switch wires, especially if any switch wires were frayed or worn through.
If you are going to use this as a mower, you really need to re-install and reconnect the safety switches -- one for the clutch pedal, one for the deck engagement, and the seat switch. The clutch switch will be under the frame, activated by a tab on the clutch-pedal cross-shaft and the deck-engagement switch will be under the dashboard, activated by a tab on the blade-engage arm.
The easiest way to re-wire your unit would be to get a complete harness from any boneyard Husqvarna, Sears/Craftsman, Weed Eater or Poulan lawn tractor -- Husqvarna makes all of them (except recent Sears/Craftsman mowers that can be made by MTD or Murray). On Sears/Craftsman units, if the Model Number label under the seat starts with a '917', it's a Husqvarna-made unit.
Hope this helps. Good luck!
Respectfully,
Rodney Rom
Rom's Reworks
Butler, MO