The RTE IVR has a heartbeat light. If it shuts down, the light goes off.
Also don't forget I had the same problem with a factory IVR.
Will do all the things you listed plus open the cluster up and have a look at the gauges as much as I can. Those are sort of the only thing I have little faith in because all the tests involving wiring and circuit board traces have passed.
But, the behavior was the same when the cluster was installed, so I don't think that is it either.
I'm leaning toward something that happened in the past killed both gauges. Maybe I will be able to tell once I've opened up the cluster and can see the mechanical part of them. I would just order an new OER fuel gauge if they cost half or less of what they do and I don't have an old one around here. (Don't care about the temp gauge TBH it's just part of the symptoms).