How to test that GFCI works?
The TEST button is a pretty darn authentic test
The TEST function on a GFCI is required to create a current imbalance in the sensing toroid, exactly mimicking the action of a real ground fault. (See UL 943, clause 5.15.3 for the details.)  So, you can be confident that a GFCI that trips when you push TEST will actually trip, whereas the TEST button on external testers may fail due to a receptacle being miswired in certain ways (such as Hot/Ground reverse) or a simple lack of equipment grounding provisions to the receptacle.  Note that NEC 406.4(D)(2) permits the use of ground-fault circuit interrupter protection as a safety retrofit when equipment grounding is unavailable.