Spare me the rants, because what I am going to say will seem theoretical. I adhere to it religiously.
One principle in hypermiling is 'plan ahead'. Which means peak traffic conditions, number, nature and locations of traffic lights and sufficient time margin for any sort of crap happening enroute.
On a light that is not in your regular territory, I would play safe, and coast on. If I pass the stop line before the light turns amber, I am allowed to accelerate and clear the intersection before the other morons gun their vehicles. If you are not that fortunate, just kill the residual momentum (would not be much anyways), to minimize losses.
If this is a familiar signal, I would have my strategy of getting through it without coming to a standstill. That involves noting the distance to the signal, noting it's status, noting which side is passing a green, and that gives you an idea of when the signal is going to turn. All this calculation does not get into the system all of a sudden, you have to practice it, and it is tough sh*t to conquer. And that is where the challenge lies.
Jumping the signal or gunning for the green are mindlessly are far inferior options. Choosing between them is sorta asking "would you like a lump of clay or a bit of gravel will suit you better?" No offense intended, it is just my attempt to clarify!
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