If you'd rather not undo your phone setup (might be desired if it's still in use for a landline) you can connect to one of the unused pairs in the cable of interest, assuming the typical voice on 4,5 blue/white setup, other pairs not punched into anything.
Either strip the ends and clip on to a different pair, if your toner does that, or pull the blue-white pair from the one jack you want and punch in one of the other pairs (or all of the other pairs) and connect your toner. I've done it with a 9V battery connected to the pair of interest and a voltmeter, in the absence of a toner.
I'm making usual assumptions (house is not wired for multiple phone lines, standard use of colored pairs, etc.) which could be subject to revision if you post pictures of what you actually have. You may need to upgrade the old 8P8C jacks to 5e or better for fastest ethernet speed you can get from the cable you have (it might do gigabit, even though it's only 5. But older jacks might limit it to slower speeds.)
Now that we can see pictures, it looks like whoever put this in punched down everything. However, the green and brown pairs are not interconnected so you should still be able to track down the cable you want without disturbing your remaining analog phone line.
If your tone tester has alligator clips, (most pictures for that tool description show a set) clip them on the 66 block where a green or brown pair attaches, [so one to the green (or brown), one to the white-with-green (or white with brown) right next to it] and then find the cable they go with in the house. Update/improve/clarify the labeling if it does not seem to match what's there. I'd expect one of the ones labeled MBR would be your best bet for the master bed room. That way you don't have to mess about with disconnecting wires at the far end, nor tearing up your extant analog telephone wiring that's still in use.
The wiring to the jack will, at minimum, need to be removed, have the twist restored, and be reconnected, even if that is a 5e jack (which it isn't, being from 2000 - so get some 5e or better jacks.)