I'd impose far tougher penalties on motorists, of which I am one, because every year that goes by people take more and more of the **** because, well, they mostly can.
Jumping lights is now standard, but it seems that people are getting ever more confident. Jumping on amber was always common. One or maybe two jumping once a light has gone red was growing. Now I can see maybe three cars, vans or even lorries/buses (going at some considerable speed with NO way to stop if they find themselves facing something now coming from a side road) jump.
But that doesn't mean cyclists, of which I'm also one, should ever be let off on the basis that motorists also break laws and are in control of something far more dangerous.
While there's an obvious link in terms of offences, the two things are still not in any way connected. Cyclists, for one, will jump red lights at ANY time, so it's harder to judge what a cyclist will do than a motorist that you just accept will jump when they've just changed.
Traffic lights, and certainly pedestrian crossings, factor in a delay to try and cope with people jumping the lights. But no crossing can work out how to cope with the cyclist that sees all red lights as give ways, or ignores them completely depending on how cocky they are (i.e. pushing through people - which does happen - or weaving between traffic, which also happens and I have to sort of give credit to the balls that these people must have given the likely outcome of misjudging).