it could be a few things but i would start by checking the wire connections at the switch to be sure they are secure and not corroded or broken. also the switch itself may be bad. check to see and replace .
The B&S Vangaurd engine requires periodic valve lash adjustment (100 hrs by schedule). Overdue valve lash adjustment typically manifests with starter stall (starter engages, rotates engine, hesitates or stalls, and then spins/starts).
The safety interlock system is designed to prevent the engine from starting unless: • The PTO is disengaged. • The motion control levers are in the brake position
You have to check both arm switches and PTO switch. AND somewhere/how there's a automatic park brake switch but I'm not locating in assembly drawing. If I've got the right model, you should hear the automatic brake deactivate when you pull both arms in and then set brake (default) when levers pushed out.
Make sure nothing is interfering with auto-bake. Once all the interlocks are satisfied, rotating off/run/start switch to start will energize starter solenoid.
Operator and service manuals available free from Toro.
https://www.toro.com/en/parts/partdetails/?id=27013
