Well, you have edited your post because your original said “other than saying it is the law / what you should do”…and limiting the responses available to others is not indicative of someone looking to engage in good faith discussion (nor is passive-aggressive responses).
If the light is broken, or you can’t trigger the light change, it would be prudent to treat it like a stop sign and stop, then proceed if it’s safe. That’s how we treat those conditions.
People in the paceline still have a responsibility to pay attention. They should have seen/been aware of the stale green and been prepared to stop, if necessary. They’re simply inattentive and irresponsible IMO.
I agree that the sensor would be activated by a car. But not activated really quickly.
In a car I would approach the red light, activate the sensor, come to a stop (or much much slower than the speed I’d been travelling at) and then the lights turn green and off I go.
Disclaimer - I’m not an engineer and don’t have a deep understanding of how induction loops work.
That said, I have been told that induction loops should work even for bikes and have had positive experiences where when this clearly hasn’t been the case (I.e. Sat on red as lights go through at least one full cycle) I’ve contacted the relevant council (UK), had messages back to say one of their engineers has investigated and fixed the problem, and then lo and behold the next time I use that light it changes for me even with no car behind. Worth a try at least if it’s a light you pass regularly.