Perhaps a newer tester, such as an Amplitrex would have the testing specifications for the KT120/150/170 family of tubes, but older vintage testers (Hickok, Triplett, Simpson, etc) most certainly wouldn't, since those tubes weren't introduced until the 21st century. I think if you knew the tester specs for a KT88, one could likely infer the testing values for the KT120 based upon its essential characteristics, since the pinout is identical.
Tube Tester Kt120
Have amplifier using lots of Kt120 on the way
Want to Test the tubes Before I fire the amp up as tubes get brittle from shipping
What is the cheapest tester for real world voltage test