Well, it would almost always be the rider's fault, since it is the rider's responsibility to treat a red light as a stop sign, and to ONLY PROCEED when safe to do so.
Riders have a little more incentive to be cautious, 'cause it doesn't much matter who's fault an accident was if you're dead.
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I was referring to accident with two participants, regardless of the vehicle type. If there is a rule that red light strictly means "STOP UNTIL IT TURNS GREEN", it is much easier, especially with witnesses, to prove guilt. When I had an accident on a crossroad regulated by traffic lights (the guy ran into me from opposite direction, hitting me with his car on my lane), the court ordered the company running the traffic light maintenance to present a traffic light plan with exact duration of various lights, dynamics of change etc. I had two traffic court experts who proved that I was driving at my green light while the other guy slammed into me when he was supposed to be standing still at his red light.
In Tennessee situation with "relaxed red", such situation would be much more difficult to be evaluated.
Yet, there is one situation where I agree that regardless of the light, driver should be allowed to proceed, provided that there is no car on the main road. This is turning right situation. Very often I have to stand still and wait for a few minutes, even though there are absolutely no cars coming from the left. If there is no additional green arrow, and often there is no because it is a "less important" road with lower traffic volume, people are standing and waiting for no reason whatsoever.
In all other situations I think that having "relaxed red" light traffic rule is like playing Russian roulette.