To be clear, I have driven the car and used cruise as long as I hold down the steering wheel button. when I release the button, the cruise disengages.

I use to see this all the time......replaced a ton of on/off switches on steering wheels(I am talking about the on/off switch on the steering wheel itself, not the on/off switch on the lever)....if it works as long as you hold the button down, you need a switch....

I did go to a salvage yard and got an identical steering wheel switch from another 2002 LeSabre, installed it on my car and the cruise still doesn't stay on. I had already disassembled my switch to see if it had a latching mechanism inside that was broken, but there isn't any, so the switch itself has no way to hold the cruise on, it is just a simple momentary contact switch that apparently acitivates something in the car to keep cruise on. Maybe some models have a latching switch, but it appears that this model doesn't, unless I'm missing something. And I have other problems:
1. The A/C will not stay on if I leave it in AUTO mode, shut off the car, and then start it again. I have to cycle it OFF then back to AUTO to get it to start up.
2. None of the buttons on the center console (radio module and HVAC module) are illuminated (they have small bulbs behind them), but none of them come on so I can't see them at night, and can't believe that all those bulbs are burned out. The LCD displays do work, but the backlighting doesn't.
I suspect these are symptoms of a control module somewhere that is going bad, or some electrical connections that are not working somewhere under the dash. If I could find a wiring/circuit diagram for these items it would help me diagnose these problems. I have found some diagrams for other years, but not for my 2002 LeSabre, which apparently is a somewhat unique design.

It IS a latching switch for the cruise.

OK, I will pursue a new switch - they are quite expensive and I had hoped to save the cost, but maybe no choice. Thanks a lot for all the help.