Is the fuel level sender on the same circuit as the low fuel light?

Just last month my fuel level sender quit working, so my 1999 XJ says the fuel level is always empty.

However, the low fuel light is not lit. I've just been refilling it with gas every 200 miles, but I'd like to buy a new sender and fix the problem. So I'm trying to run it as low as possible to lessen the weight of gas in the fuel tank.

Is the light that triggers low fuel level on a different sensor/circuit as the fuel level sender?

I just wanted to make sure before I do something dumb like drive 275 miles until the thing dies on the side of the road on me.

My cluster is the type with the tach like this. Not sure if that matters or not.

On the 91-96 models there is a little module inside the gauge cluster that trips the light when resistance from the tank sender drops below the 1/8 threshold. Dunno on the later years but I assume it's embedded in teh ECM logic for 97+