That's certainly a good option.Personally I think i'd have gone down the comparator route, I've done something similar with a comparator (may have been a 339), a zener, a handful of resistors and a 2N2222 to drive an NC relay........ The primary reason for this was low quiescent drain (down to several uA, as it's for a vehicle),
But an LM339 takes more than several μA, more like 800μA (which is still a very low drain).
And there's also current for the zener and other bias currents.
Below is the circuit with an LM339/393 comparator.
Take your pick.

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