Regarding the red triangle & clearing the message. If you get a System fault with the giant yellow triangle in place of the clock you can clear that 100% of the time however if you are getting all four tires flashing that's a hit or miss. Sometimes you can & other times you cant. If you have a module or receiver going bad with intermittant problems like I had you get it both ways. Just wanted to assure the OP that he's not crazy. That error will not always trigger the triangle on the screen. Personally I feel the whole TPMS system is a joke on this car. I've had older cars with much less tech have superior systems. C5 corvette's for example will show your pressure right on your info screen.
Then again, Jaguar feels we didn't need temp gages, voltage gauges etc.... so not surprising.

 

Those are the "Idiot" lights on the tachometer that light up amber. Dude was talking about the Text Alert between the Tach and Speedo taking up his clock space. The only thing red is the triangle on the touch screen.

 

Yes, we are talking about the same thing. The red triangle doesn't always come on for this particular fault. I speak from experience on my own car (as I type this its happening). I have a bad module that's intermittant & when it gets into it's mode where it's not working I will get the car image between the tach & speedo with the four wheels flashing in red. Sometimes you can clear it at the infotament screen & other times you cant. If the OP is not getting the symbol to clear at the inforament screen my money is on a bad module.

 

The red triangle comes on with the message that the tpms has lost contact with a particular tire. In my case it is the RF. It happens to me maybe weekly and then clears itself anywhere between 5 mins to 2-3 hours. I clear the big warning to get the clock back with the little red triangle on the bottom of the infotainment screen. I have had the same issue in each of my XKs and I have two different dealers try to correct it. Since my 13 is still under warranty they have replaced the main tpms module twice. Still same issue.

 

Right-Front.... you may have the "Pinched Wire" syndrome, whereas the bumper mount inside near the headlight area on the inside of the bumper has the wiring harness for the TPMS antenna pinched between the mount and the bumper. It's easy to check, just undo a few screws and slide the headlight out and take a look, it's easy to spot.
There is at least one thread on here dealing with exactly this.

 

Thanks, but the dealer keeps telling me that is not the case. I do mention it when I call their attention to the problem.