I'm driving, stopped at a red light and in the left turn lane. A fire engine comes up behind me, siren blaring, lights flashing, pulls behind me and lays on the horn. What do I do?

Fair enough but that can be a big ask of the driver in front of the fire engine.

There are all sorts of intersections and some it is really easy to see if it is safe to cross. Others, not so much. But then you have a fire engine urging you on.

If you enter the intersection (because of the fire truck) and a car crossing the intersection on a green light hits you…who is at fault?

I would say you and the fire engine driver, jointly.

It would not surprise me if it’s technically illegal in most jurisdictions. It’s difficult to craft a law that explicitly allows this, without fuckwits trying to use it as an excuse to run a red light when they hear a siren half a mile away. You need to ensure there’s a strong burden on the driver to only do it when absolutely necessary, and to be absolutely sure it’s safe. It seems to me like a situation where you just need to make a personal decision to technically break the law if you’re completely sure it’s safe to do so, and trust to common sense that you won’t be prosecuted for it.

Having right of way doesn’t normally mean that the other driver can break the law to yield right of way.

Here, a driver who hits another vehicle is considered to be mostly at fault. They should know to be careful at intersections with emergency vehicles in them.

The drivers to your right should have started merging to the right, and then you move to your right into the ‘straight’ lane - then after the truck passes, you get back into the turn lane.

You are not supposed to break the law (run the light) to get out of the way - EVERYONE is obliged to move over.

I would be surprised that the emergency vehicle did not go into the opposing lanes (against traffic) in that situation.

This is exactly why you do not ‘run the red’ - the emergency vehicle may be allowed to - you are not.

They will if they can but it is a busy intersection and, often, the lanes going the other way are filled.

So if there’s no traffic anywhere in sight that would create any risk of an accident if you pull through the junction, you’re just going to sit there blocking the fire truck until the light turns green?

Yes, you have some liability if you do cause an accident. You have a responsibility to be safe. But that doesn’t mean the right thing to do is just mindlessly sit there.

It does here, under statute.

So in this case you’re not violating the law if you turn left against a red light. In fact you’re violating the law if you don’t get the hell out of the way.

If there is no traffic anywhere in sight - the firetruck won’t sit behind you - it will move into the opposing lanes and travel thru the intersection.

In that case - you sit still so the Firetruck driver can anticipate what you will do.,

To address your last point first–some streets have large and/or high medians leading up to the intersection. I’ve seen medians that even a large, high firetruck may not be able to easily or safely get over.

To your first point–
What if the drivers in the right-most lane have no shoulder or turn lane to move on to? What if THEY are boxed in by a curb & sidewalk? How are they going to make room for other drivers to clear a lane?

There are times when running a red light is the ONLY physically-feasible option.

That’s for a vehicle already in an intersection. We’re talking about a vehicle right before the intersection.

In that case - you best be patient - or move to the right (move ahead of the traffic blokcing you to the right) instead of taking the left -

Well, someone there could take a perfectly legal and safe ‘right on red’ to make room

From a dedicated left turn lane, that is no more legal (and certainly no more sensible or predictable) than just making the left turn if you’re sure it’s safe and the junction is clear.

Here’s the official word in Missouri:

You must yield the right-of-way to police, fire, ambulance, or any other
emergency vehicles using a siren or air horn, and a red or blue flashing light.
Pull over to the right edge of the road, or as near to the right as possible,
when you see or hear an emergency vehicle approaching from any direction.
If you are in an intersection, drive through the intersection before you pull
over. Remain stopped until the emergency vehicle passes. Follow any
instructions given over the emergency vehicle’s loudspeaker. Emergency
vehicles may follow each other so proceed only when the way is clear.

(Emphasis added)

From your cite:

Drivers in Arizona are required to yield the right of way to all emergency vehicles with illuminated red or red and blue lights and sounding a siren, whistle or bell. When an emergency vehicle approaches, you are required to immediately pull as far right on the road as possible and stop your car parallel to the curb or edge of the road. You must remain stopped until the emergency vehicle passes, unless a police officer directs otherwise.

You have to pull to the right as far as possible. Doesn’t say anything about turning left on a red.

In the OP, the driver is not in the intersection. He’s waiting to enter the intersection when the light changes.

From your Port Arthur cite it is illegal to go through a red light unless a police officer authorizes it.

And the officer is careful not to say you should move against the light.

The OP is not in the intersection when the fire engine comes up behind him, so I don’t see how that applies.

Not really. That’s just saying don’t pull over in an intersection. The doesn’t tell you what to do if you are already stopped at a red light and the emergency vehicle comes up behind you. Everything I’ve found just avoids the issue, and I think for understandable reasons.