I had a similar situation at my house. Wife wanted bathroom redone. Changed colors of walls and floor. I wanted to change Ivory colored GFCI and light switches to White. So I pulled a perfectly functioning Ivory GFCI and installed a White one. It would trip the breaker upon being reset. I tried a 2nd GFCI. It wouldn't work, either. Reinstalled the original. Nope, it wouldn't work either. Scratches head. Buys GFCI tester similar to yours. Got all three lights, which wasn't on the list of possible combos. YIKES@$%%#!!!
So I started tracing things back.
First, the circuit breaker was faulty and burnt inside.
Replaced breaker.
GFCI would now reset OK.
Tester down to two lights, but flopped polarity.
Followed wire to next box in circuit, a ceramic ceiling light fixture in the basement. Found smoked connection in that fixture and cracked ceramic. Tested polarity at that box. OK. Replaced the fixture. Still flopped polarity at GFCI as expected.
Followed the wires to a j-box under the bathroom. Opened that up to find the hot and neutral going up to the GFCI were swapped. Removed all of the many connections, sorted everything out, re-connected properly and all tested well at the GFCI.
I still have no idea why the original GFCI was working, then no GFCI was working, other than I flipped the breaker to power off the circuit originally and that drove the breaker to finally die.
Anyhow, it was a good refresher lesson for me in circuit testing and starting from the beginning. I don't get frustrated too easily and don't mind doing that kind of work. It's just a logical trace-out from beginning to end. Slow and methodical. The only bummer was it was all overhead work, so my arms got tired after a while. Just another excuse to take a break and have some snacks.
