GFCI won't trip with tester

A bit baffled on this one. Checked a GFCI today in a guest bath that wouldn’t trip using a simple Amprobe 3 light tester. The light wasn’t on in the outlet but it had power that according to the tester was wired correctly. The outlet tripped when the test button on the outlet was used and then reset just fine.

Then the part that really got me, the outlet tripped using my amprobe tester on a downstream outlet in the master bathroom.

Is this just a case of a bad GFCI that should be replaced? Thoughts?

You may have an open or non existent ground.

This is also my guess.

how old is the house?

I thought open ground too but then the three light tester should have indicated open ground.

I had a similar issue. In my case the ground was bootlegged so it didn’t register on the 3 light tester.

Usually a ground issue or bad GFCI