I can tell you how it works.
When you turn the key on, it checks for signals and gets a reading.
Im not sure how it determines which wheel is which, but a tpms reset tool can read the pressure, so whatever signal is being sent prob has code for both the pressure and an ID for what ever wheel you have it programmed to . All that is if it will tell you which wheel is low. If the system wont do that then it is prob just one signal for pressure.
Ok so you turn the key on it gets the signals and a pressure reading and if it sees low pressure it turns on the tpms light. If it does not see a signal at all (not just a low pressure signal) from one or more sensors then it turns on the tpms light and some other tell tale for a problem with the system. This is monitered every so often ( cant rem the time frame).
Built into the sensors is an acceleromter, as soon as the wheels start to turn they send a signal and the system starts to monitor the pressure every 30 seconds. If you were to try and trick the system with a pressure tank, this is where it would fail. The bcm would detect a wheel speed signal from the pcm or other modules and not get the we are moving signal from the pdm (passenger door module). It would then activate all the tell tales.
So in order to trick this your pressure tank would have to rotate. You would also prob have to have only one sensor in one tank. So that when you set them up with the tpms tool they would be for just one sensor.
So to fool this system with a pressure tank you would have to:
Make four tanks, one sensor for each.
Rig them to rotate
Use a tpms tool to calibrate them apart from each other.
If the rotation part was not there you could put them all in the spare tire and tape them equally apart and air it up and then calibrate them. Might work
On older systems without the rotation check.
The easiest way to beat this system, is not beating it at all and just getting them in the wheel somehow. Even if you had to duct tape going around the wheel. Or make some kind or retaining clip that would allow you to attach it to a big hose clamp. Older Vettes and other oems used these and you can buy just the clamp if need be. IF it were me, this is what I would do. As just about any other option is gonna cost more to bypass the system than just work with it. Even if you are buying sensors every 7 years.
Another way would be to get something that can read the signals. Then build a programble board that will transmit these signals. Tap into a wheel speed signal off of the truck and program the board to go into rotation mode. If you did this you probably couldnt build enough to keep up with people buying them. That is if it were not illegal.
Another way is to find a programmer that can flash all of the needed modules to just turn it off. Im sure it can be done, but all of the equipment needed to flash a module not named pcm is gonna be hard to find in the aftermarket. Even if you had a buddy that worked at a dealership, with all the right stuff, there still might not be an option to disable tpms. Any module that is on the vehicle has to flashed to rest of the modules. But when you do this with factory or aftermarket service equipment you dont have many options of the parameters. Speedometer is about the only one I can think of.
So while it is absolutely possible in the theory of any module that is flash programmable and these modules are, does not mean anybody has anything you can buy to do this yourself. When you buy a programmer for your engine, some one has hacked the pcm code and changed the values to whatever need be. Has anybody hacked a bcm? What about the PDM? That is the problem with that method. Cant be a lot of demand for that.
The only other way that would work in theory would be to program all the modules to a year model that does not have the system or a model that does not have it. You might even have to have different modules (more to buy) . This is gonna be highly unlikely that you lose tpms and not other stuff as well.
Or you stroll by your local dealership and ask them if they can turn it off and if they can, pay them to do it. There could be the option to turn it off with their flash programming systems. You never know.