Every home inspector should have one. It could be used for the Standards of Practice at Home Inspection Standards of Practice - InterNACHI®.
According to the InterNACHI® Home Inspection Standards of Practice, a home inspector is required to inspect all ground-fault circuit interrupter receptacles and circuit breakers observed and deemed to be GFCIs using a GFCI tester, where possible.
And here’s a big list of inspection tools Home Inspection Tools & Equipment List - InterNACHI®.
If a GFCI fails to test when using a tester, it is not defective unless it does not trip when the button is pressed, pressing the button is the only way to test a GFCI according to UL.
Rollie is correct. The only recognized testing method is the built in test button. The training should be changed to reflect this.
Don’t know if the training addresses that the indications are not always correct or that they can be fooled by a bootleg ground.
It also seems that many are unaware that an ungrounded receptacle will not trip if a 3 light tester is used.