Sorry, just now seeing this! First things first, I am not an electrical engineer. Use these suggestions at your own risk and consult an EE or your local robotics team. With that out of the way…
Long story short: This can be accomplished with a normally-closed relay.
Short story long: I would recommend disconnecting ONLY the foot pedal, nothing else (assuming you want the rest of the vehicle power to work, which is how I interpreted “the car needs to still be “on”…”
Once the foot pedal is disconnected, you’re basically replacing it with the normally-closed relay in place of the foot pedal. We use something like this. There are dozens of them on Amazon from different brands, all identical.
Then you need a switch to go on the seat. You could just re-purpose the foot pedal or replace it with something entirely new.
Ideally, you will also need a battery (e.g.: a 9-volt in a housing). Alternatively, if you are using the foot pedal and know it can safely handle 12v (at a very low draw), you could just split power off from the car battery. You will need to do some reading on how to wire a normally closed relay, but once you get it, it’s not difficult.
For a standing car like this, it’s really important to have a good kill switch. You can also wire that into (what used to be) the foot pedal loop, so that it kills just the motor, not the whole car.
If you need more help, shoot me an email at janesw [at] health [dot] missouri [dot] edu
and definitely consult your robotics team, an electrician, or an EE!