Doubt on ground reference of Isolation transformer

It's a little unclear what exactly you are trying to accomplish. If the point is just to experiment with full wave bridges and see all the signals, then do it at a low voltage like JonnyBoats said. You can probably find a old transformer somewhere that is rated in the range 6-12V AC at 1 Amp or so. That's a good size to put a full wave bridge after, and then you also get a useful DC voltage to do lots of other things with.

As Jonny mentioned, there are also wall wart type transformers that are rated for less power but you can do mostly the same things with. The advantage is that these things are cheap nowadays. You can probably find something in the 3-5 Watt range for $5. Jameco has a broad selection of such things. That's a good place to look around.

If you really want to experiment with a full wave bridge driven by a function generator, then you should power the function generator from a isolation transformer. These are 1:1 transformers meant to take line power in and put line power out, except that the output can float. These will cost a bit more since they are usually intended for 100 W or more. Sometimes they even come in a box with a line cord for the primary of the transformer and a regular output connected to the secondary. You simply plug the cord into a wall outlet, and the thing you want isolated into the outlet on the box.

One gotcha you have to be careful of with these things is that they may not come wired up fully isolated. I bunch of years ago I bought a 500 W "isolation transformer" that was just as I described above. I used it to float a device under test so that I could hook up a grounded scope to it at various places. The first time I touched the scope ground clip to part of the power supply there was nice spark and the fuse blew. It turns out there was actually a deliberate ground wire inside the isolation transformer box connecting the ground from the line cord to the grounds on the output sockets. That's not what I consider "isolation", but someone else apparently does. Once I disconnected the two sides of the transformer and carefully verified there was no conduction path, it worked as intended.

That's the correct indication for the transformer in its original configuration.

With a normal outlet, the neutral and the ground are bonded together at the service entrance, so the tester will light two lights: one between line and neutral and the other between line and ground, since the same voltage appears across both pairings.

With the tester plugged into the transformer, there's voltage between line and neutral created by the transformer secondary, but now there's no path between your isolated neutral and ground, so now that light on the tester no longer lights, indicating "open ground".