Spare cloned TPMS setting off warning light?

I got a new set of wheels for my 2011 Tacoma this summer, figuring on using the original wheels for winter tires. I put a set of Autel cloneable TPMS in the new wheels, and everything programmed fine (I did the same with my Sienna at about the same time, with no issues).

When I got tires mounted, I had the old wheels in the back of the truck, and had a TPMS light come on all the way home. The tire guys suggested it was because the truck was picking up two different sets of sensors with the same IDs, so I figured the issue would go away after the old wheels had been off for awhile (I assumed the wheels would stop transmitting eventually). Sure enough, after I dropped the old wheels in the garage, about a mile into the next drive the TPMS light went off...until I came back to the garage.

Nearly two months later, every time I start the truck I have a TPMS light. It shuts off about a mile down the road, and turns back on when I get to the front of the garage. It's a minor nuisance, but if I do have a low tire I would like the the warning light to mean something before I'm away from the house. Do I need to wrap the old wheels in foil, carry them to the basement, wait another month, or what?

 

A further thought... Would the fact that the original wheels no longer have tires on them be the issue, rather than the fact of having two sets of sensors with the same IDs? Maybe it's less the number and more that half of the sensors are reading only atmospheric pressure?

Still, I would think eventually the sensors on the wheels just sitting idle would shut down to save power, wouldn't they?

 

Sell the old wheels or store them away from the truck.