It is the tip that has the two dissimilar metals fused together that provide a small electrical
current when heated, proportional to the amount of heat. The length of the tail has no significance.
As long as the connections to the sensor are intact, the thermocouple is functional. The main problem is the current level is very small, so any discrepancy in the the end connection can cause it not to work. Cleaning that tiny connector almost always corrects the problem.
On a recent trip our gas refrigerator
wouldn't stay lit. All I had available small enough to clean it was a tooth pick and some auto paint
rubbing compound. A minute of swirling a tiny bit of compound around with a blunted tooth pick did the trick and the refrigerator
I doubt this is a recommended procedure, but it worked for me in a pinch. So if you do it, you are on your own!