After multiple tries, I was able to get the TS501 to trigger and read one of my original tire sensors from the tires on the car. It was not able to trigger and read the other three original tires. The TS501 said the one tire had a low sensor battery. It might be possible that the other three had bad batteries. This seems unlikely since I was able to read the tire codes using the ODBII port, but I'm not sure.
I tried to get all four of my winter tires to trigger and ready, but I was not able to get them to. The winter tires were not on the car yet, but I will put them on the car and then try again. I'm not sure if that would matter.