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I think the light coming on was your clue. I would have tried to stop sooner than 10 minutes after it came on. Many tire punctures drain out the air quickly and you won't have 10 minutes of driving available. Others will be a slow leak. I would treat any TPMS light as an emergency situation until the tire situation can be assessed.
I agree, but in previous blowouts the car would usually start to drive funny or something. I noticed nothing until i came to a stop then tried to pull off again. I know better now though.