Water temperature gauge flutters

If this is the only gauge that that behaves this way? I doubt if it is a bad cluster because I see that gauge shares power and grounds with other gauges, but that does not mean that just that gauge is not bad. I suspect though either a bad gauge or the wire is loose and/or making a bad connection or partially shorted. After the engine warms a little until the gauge registers some in order to check it, wiggle the wire from that "thermal transmitter" located top left side of engine all the way up to the cluster connection and see if you can make the gauge fluctuate when you wiggle the wire. You may need a helper to watch the gauge. If you find a spot that makes the gauge move, check that spot for being loose and/or shorted and if you cannot find anything, and moving it does cause the gauge to fluctuate, the wire strands inside the wire may be broken, so replace the wire.

You are welcome.