Yep, go to South Wheal frances and find Daubuz engine house (one with a flywheel loading down the hill from Marriots) in front of it about 20m or so is a shaft tip, if you climb up it, you'll see how far the water is down. I believe it's hugely variable. It was about 10ft down when I was there last, although I gather it can go down by well over 100ft.
If you do happen to have a peer down this shaft, report back, I'd be interested in knowing.... It's been pretty dry for a while. Water should be right down.
Flat lode stuff is the most interesting in the area for surface remains. If you want to chuck rocks down holes, Consols is the place to go (Gwennap). A lot of the stuff around Carn Brea has been well sealed up or made very secure indeed.
I'd be inclined to go and poke around the copper district....