I don't usually shut the engine off unless I've been through a particular intersection atleast a few times. I feel like enough lights have enough different patterns, that I leave it to learning/confirming how each individual intersection works.
Having an auxiliary starter button helps a lot getting caught flat-footed(engine off at the front of the line when the light turns green), and I can get restarted and take off as fast as many drivers loosely paying attention to the light
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