Adding a full size spare with TPMS to 2024 ES350

[MD2595]

I bought my wife a 2024 Lexus ES350 back in May.  I hate donut spare tires so every vehicle I own has a full size spare.

I bought a matching spare OEM Lexus wheel, Bridgestone OEM tire, and I called the dealer and was given TPMS part number 5500117 (Denso).  I had the everything installed and at the 10,000 mile service the new spare was rotated in.  We were heading to dinner last night and about 30 miles after the rotation the TPWS system light came on and a message saying take the car to the dealer appeared.  The car would not read ANY of the TPMS sensors as all of the tires showed dashes.  After stopping and conducting a visual inspection of the tires, all appeared to be fine and the trip was continued.

Today I took the new spare off and re-installed the factory tire.  Within a couple of miles the system reset and the warning light went off.  The system was now reading all 4 tires as normal.

I did some more research and found another part number on parts.lexus.com but when I pulled up the number (42607-OE020), the website says "THIS DOES NOT FIT YOUR 2024 LEXUS ES350".

I found another part number on www.lexusoeparts.com of 42607-53020.

Has anyone had success with adding a full size spare with TPMS? 

I was told my the Lexus service manager that the ES cannot be programmed to read 5 wheels with TPMS, and I was told at Discount Tire that the new Toyota/Lexus is a learning system that reads whatever TPMS is put on each position and it is not necessary to "learn" the computer like in other makes.

Thanks in advance

Edited Sunday at 06:17 PM by MD2595
Adding info