5.3 idle is 600 I think this is low and sometimes the idle pulsates. on 2003 Chevrolet Tahoe

Have used at least 1 gallon of additive/injector cleaner has NOT made any difference. Took it to AutoZone checked the computer for codes NONE. Runs fine once you get away from Idle.

Asked by for the 2003 Chevrolet Tahoe
By now you have probally done damage to the fuel system with that much additive. You need to have the air induction system cleaned. Have a professional clean the throttle body, Mass airflow sensor and intake with an approved cleaner.
What type of damage would have been caused?
Yes in your climate it is necessary to have coolant warm the throttle body because of the cold temperatures in the winter.
I live in southwest Florida. You really don't need throttle body warming here.

Please do not play chemist with additives. More is not better.
2 more answers , 1 more comment
idle speed control motor could be malfunctioning. throttle body could be dirty as well. you need a shop with a real tech and a real diag. could be something simple.

clean throd body with carb cleaner with engine off open throdle wide open spray inside and wipe out with a rage dont use straw it might go into intake
Today I removed the throttle bodyand throughly cleaned, it was very dirty also changed the air filter. I will see how it reacts over the next couple of days. And whats with the coolent connection on the bottom of the T-body? does the coolent cycle around the T-body?

Today - I don't know if my tach is wrong but my idle is now 500.