A different TPMS problem

[Georooney]

My 2005 Xterra TPMS light never comes on around town, but does come on after 35 minutes of highway driving. (You can set your watch by it!) Stop the Xterra, turn it off and restart it, and you're go to go for another 35 minutes when the light pops back on again.

I know, you're going to tell me to check my tire pressures, right? Been there, done that, got the T-shirt. No joy. Well, here's the thing. I'm now running winter tires on steel rims, with no TPMS sensors installed. In other words, there are no sensors to send any kind of a signal to the module. Exactly the same problem! I suspect the module is hooped.

I'm told there's no way to disable the TPMS, so other than sticking a small piece of black electrician's tape over the light does anybody have a suggestion?

Thanks in advance.