Water temp gauge

I have a 1989 Jeep Wrangler Sahara, 6 cylinder 4.2L, 5 speed with 116,000 miles. When cold from sitting and I begin driving, my temp gauge would go up a little bit then jump all the way to the right maxed out. I replaced the sensor at the rear drivers side of engine. Now it goes from cold all the way to maximum hot as soon as the engine begins to warm. I have no overheating problem. I've driven the car 50 miles at a time many times with no problem.

How can I test the temp gauge to make sure it is or is not broken? The dealer says they don't have new ones available any longer.
Any ideas?

Thank you for your help