Car overheating fans not kicking on

It is no trouble at all.
I saw that video and the way that needle jumps up makes me think it is not running hot. It is an electrical problem. A bad temperature gauge or sensor. Does it have a check engine light that is stuck on too? If so, you should definitely have it scanned for code numbers. Even if the check engine light is not on, that coolant sensor should be checked with a scanner or an ohmmeter. It is probably a bad sensor, but I could not recommend replacing it without scanning or measuring it with an ohmmeter first. https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Since you have a scanner you can see temperature data and temperature gauge at the same time.
So when the data reads normal and the gauge jumps up. Retest with another temperature gauge.

Well if it only shows codes then yes you can test it. But they also have an option where it shows data and that will show exact temperature.

You say you removed the needles and added an overlay to the dash and after that this started correct? I would say the issue is the stepper motors are failing and the cluster needs to be repaired. Very common in that vintage to have the stepper motors fail, especially if they were touched at all. There are kit's and places you can send the cluster to for repairs. I do not recommend DIY unless you are very skilled at circuit board repair as the boards are not very rugged and unless you are extremely careful you can damage the board itself.

Just do not want to see you chasing overheating or other issues if it is a bad reading on the cluster.

That is the issue, if the stepper is failing it could read wrong. With the fuel stepper being bad it is a real possibility. When you shut the car off and then turn the key on, where does the needle set? Does your scan tool read live data? If so compare it to the gauge.

How about for the temperature gauge?

If it is not smoothly rising from the low mark as it warms up you have a bad stepper motor or a bad head gasket. The coolant is not going to suddenly heat up and cause the gauge to jump. A bad thermostat would cause it to simply either heat up rapidly until it boils over or if it fails open it will slowly heat up and probably set a code because it does not reach the control temperature in a short time.

Does it actually overheat to the point it boils out coolant? Or is it only the gauge? How about using an IR thermometer to check the temperatures at the block and hoses. That would tell you if it's real or related to wiring/cluster/sensor. The #93984 that HF sells is accurate enough for that testing.