I think when you took the other tire AWAY from the car for the repair, it lost the signal and that's why it is blinking. IS there a reset in the manual? That, or the one in the spare doesn't work; did you put the original tire back on? You also can't use ANY fix-a-flat or other stuff in the tires with these TPMS sensors in the rim, it clogs them up.
Anyhow, yeah, the light in my Vibe blinks too, but that is because I removed the $180.00 sensors from the wheels. I was going to buy tires at Sams Club, but one sensor was damaged, the threads for the cap. Someone put the wrong sized CHROME cap on, and crushed the top of the valve stem, and he could not get the valve out. It was leaking a little so it had to be replaced. Well he could not get the thing out, so, we called the dealer, and they wanted $180.00 for the sensor. We said, FORGET THAT man... Sams would not proceed any farther, and would no replace the sensors with regular valve stems. AND, NO other main-stream car place (PepBoyz, NTB, ect) would remove the sensors, and replace them with regular valve stems. They said, since it came WITH it, it HAS to have it. The guy at Sam's told me, any car 2006, and above, has TPMS, due to the ford tire blow-outs debacle. I said, yeah, funny thing about that? I got a 2006 Liberty, no TPMS!!! He said "Oh, that's odd." I also said; that ford tire issue was due to badly made tires from FIRESTONE/BRIDGESTONE, in which they would normally not blow out if slightly under inflated, it was a DESIGN FLAW. He said the TPMS systems were made BECAUSE of that, yeah sure... I think he was full of crap with those two lines... So, I just bought the tires, no warranty now, and took them to a regular mechanic to remove the sensors, and put regular stems in, and mount/balance the tires. Originally, the light was SOLID with the sensors sitting on the front seat. I brought them in the office, now it blinks for about a minute, then goes solid...
Yours is acting like a sensor is not being read.