You have found some good stuff here. I would not give up on this area yet. If anything it is fun to get out in the woods and explore and get the blood moving. Those carvings in the tree led you to that cave/mine, that is huge in itself. At one point it could have been completely hidden, someone in the past found and opened it up.
Someone asked why there would be carvings on the tree if the mine ended up nothing and they gave up on it. The carvings could have been used just so they knew how to get back to the mine while they were digging it, as that would have taken some time. So that is one realistic option, it turned out to be nothing...
But for fun, icefly could be onto something. The end of that cave does look to be somewhat cemented, or caliched or whatever it is called... And the map on the tree showed 3 different chambers all connected in same tunnel. But there is no way I can condone you somehow knocking that wall down to see, will be extremely unsafe. or maybe drill through for some kind of verification on how thick it is... if it opens up into a void, etc. But my god be careful if you do any of this, actually I am officially telling you not to do this
You can at least and should metal detect the heck out of that cave, maybe even with a deep seeker. Wouldnt hurt... I know certain detectors can find voids in the earth, maybe they can find voids through the caliche on other side...
ramblings over