As it happens on idle and I'll assume clutch disengaged that rules out for me props and UJ's. Injectors are pretty bullet proof on the 1KZT from everything I've heard.
Your blind fella with his super sensitive ears says engine is running sweet as so you can rule that out too. So it seems to me that external factors would point to an engine or gearbox mount getting a bit old and squishy and creating a little imbalance that way (no real way of knowing without changing them all I guess), a slight stretch but maybe a broken or sagging spring.
Internal factors would lie engine side of the clutch, so worn spigot bearing, worn crank bearings. Can't see it being flywheel unless chunks are missing from a worn clutch in its history.
If the timing tensioner pulley or water pump were old and giving up the ghost then maybe adding a hit or miss resistance likewise aircon bearings.