TPMS, is there a way to test it before installing?

There is no real way to test them with your vehicle that won't cause the TPMS to become a problem. The TPMS on your vehicle reads the presence of each of the 4 sensors. The sensors turn on with the rotation of the tire or by using a tool to turn them on. However, the system can only read 4 sensors at a time. So, to test the new ones you would need to remove a tire and put it far away from the truck. Then activate the new sensor and see if the truck reads it properly. The catch is now that you need to put the tire and TPMS sensor you took off back on and hope that it still reads that sensor until you get to the tire shop, but the OE sensor requires initialization so the light will likely stay on. Many of the new sensors for that truck come programmed so I suspect they will work.

They have a tiny accelerometer inside them that tells them when the tires are rotating and to turn on. Then they transmit their ID and pressure to the vehicle. That signal is read by the vehicle with the ID telling it where that sensor is and what the pressure is. So, sensor ER35490 in the left front tire will be reported as the LF pressure while sensor GT34065 in the right front tire shows the RF pressure, the other sensors will also be coded in a similar manner. Normally what happens with ones that are pre-programmed is simple. They get installed in the rims, tires get put on and installed. On some vehicles you just drive it around the block and the sensors wake up and the pressures are read, and you are finished. On OE type sensors for your truck, you use a tool to read the sensors ID and use a scan tool to enter that number into the vehicles TPMS system, now it knows where that sensor is and the tool that reads the ID will wake it, so the system locks in its location. I believe the ones you have are simply the OE design that uses the reader and scan tool to initialize them. The "no programming" in this case just means you don't need to use a tool to tell it the frequency and vehicle ID like the universal sensors they sell. So, these are already set on 315 mhz and with the correct data stream for a Toyota. They still need to use the tools to set them up once they are installed.

Normally they would install them on the vehicle, then initialize them as installed. That tells the vehicles systems where each sensor is located. You will still have the warning light because the other sensors are bad.

They would put them on the truck and activate them. So, say they put one on the right rear and the other on the left rear. Then they activate them and check that the truck reads them in those positions. Then when you get the other tires, they will do the same with the other 2 TPMS sensors when they install those on the front.

Well, they should be able to do that by putting them next to the tire on the truck. Then just chalk mark them so you know which one goes where. The catch is that if the TPMS in the tire on the truck is still working you can't program in the new one because it will see 2 signals for the same location.