Keep Vehicle Running With Kill Switch Activated By Brake Pedal?

In trying to have a way to keep my vehicle running just in case I need to keep my dog inside to run in the store. Remote starts for my 2022 frontier are easy enough, but they are time limited to ten minutes I believe. I was thinking a simple hidden toggle switch to connect the brake pedal switch to a relay that would disconnect ignition power should do it. Then just leave it running with keyless start lock the doors and leave. If someone does decide to take the truck as soon as they touch the brakes it kills ignition and won't start back up because the key will be with me. I'm thinking there's a flaw in my idea but I can't quite place it. Anyone have any input or a better or more secure way to pull it off?

A remote start with "Pit Stop" mode should allow you to do this. Typical scenario.... You park the car, hit the remote start button on the key fob, and pull your key out of the ignition. The vehicle continues to run. You get out and lock the vehicle and go into the store.

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My truck uses a key fob with push button start. If I leave with the key while it's running it will just keep running indefinitely. If someone drives away with it it doesn't care. They just won't have the key to restart it.