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Planning on spinning more?? Leave your tow hook in the car, the time it takes installing it won't make a difference in the entire process.
Certainly hope not! First time was "signed off irrational exuberance". Second time was a different story (no-brakes exercise with instructor - good story, we can chat in person).
Like a lot people, I do not typically run with the tool kit/parts. Based on my experience, the last thing I want to be doing after I've disabled my car at risk to self, car, and fellow participants, is to be fumbling for a toolkit, removing license plates, threading tow hooks.
Sounds like potential stress and aggravation/damage easily prevented.