Temp Gauge swings toward high-side and back to norm with 3 sec

You would think so. The key is in the way a OEM limiter works... At switch on the limiter throws a lot more current to warm up the gauges,,, and when the engine is cold that's 1 gauge. The fuel gauge supplies the only "path of least resistance", so the current goes that way. Fuel gauge response is about the same but not considered "acting up". Once the temp sender is hot the limiter finds 2 paths of little resistance and puts out even more current through 2 gauges. Consider which is the shortest path to ground.
I wont argue. Diagnose first, then replace the limiter... soon. Good luck with it.