Yes, you are correct. But as far as I can tell, the problems did "start out of the blue". Everything went to hell when the alternator died.
I had just bought the vehicle and I did not drive it, because I did not yet have Mexican auto insurance, I spent time getting it ready to pass a California smog test. I cleaned the MAF, new Denso spark plugs, oil change, new air filter, new battery. Every thing SEEMED to be working fine. Finally got Mexican insurance and I drove it to the U.S. Waited in line for 1 1/2 hours to get across the border (at idle). Got on to the I-5 and it stopped dead. Not even any running lights. Next morning, Auto Zone recharged the battery and they tested and told me that the alternator was bad. They said I'd be able to run on battery power alone, long enough to get back to Mexico.
Got within 2 blocks of home when it died, again. Towed it back to the secure parking lot. Recharged the battery again. Ordered and installed the Amazon alternator. Started it right up and everything SEEMED to be working fine. Idled it until warmed up. THAT IS WHEN IT STALLED. I know next to nothing about auto mechanics but it sounds like I have a problem with a HOT IDLE. ????
NOTE: The only place in Tijuana that MIGHT be able to diagnose the problem(s) is the Toyota dealership. But, God knows how much they would charge for such service. $1,000 USD or more ???? I might easily spend more on repairs than I did on buying it. ???? Every other place would rip me off and THEN still not find the problem.
At this point, as other posters have pointed out, I have little to lose by removing the throttle body and IAC and cleaning them with CRC throttle body cleaner.
Being retired, I have lots of time, not much extra money, and only a small amount of knowledge.