Phantom cruise control after transmission replacement

We had a rebuilt automatic tranmission put into our 1999 Dodge Caravan about 4 years ago. Since then our cruise control has only worked three times:

Once on our way out of town immediately after the transmission repair. Again, weeks later after the transmission checkup. And one more time when a different shop tried to troubleshoot the problem. All other occasions give the following behavior:

After pushing the on switch, the “cruise” light on the dash turns green and then goes out within 2 seconds. No functionality of controlling the cruise occurs.

Both shops claim complete bafflement. But we really believe something “simple” happened when the transmission was replaced.

So how can we get the cruise control to return from the realm of the undead?

Thanks for any solutions or just good jokes.

Roy and Debra Terry, Santa Clara, CA