>>1560398there used to be a website that showed all the claims past and present in the US, but the gov took it down about 10 years ago I think.
Anyways here's what you do:
first if the mine is on BLM or FS land you just go down to your local ranger district office and ask to see the records for the location.
they'll tell you whether it's currently claimed, lapsed, or removed from mineral claim. A lot of old mines have been removed from claim on Fed lands. Also a lot of them have been plugged and capped, though yours doesn't look like one of that sort. Anyways if it's on BLM or FS and it's available to claim it'll cost you a couple hundred bucks to file on it, and there's a shitload of laws regarding how you proceed once you own the claim. Be aware if you claim it you can be sued by the EPA to plug the mine and clean up any waste there, which generally costs millions of dollars. This happens fairly often.
if the mine is NOT on Federal land it's just a private patent and you can check with the Conejos County Assessor to find out who owns it. Perhaps they'll sell it or lease it to you for a few grand. More likely they'll haul you into court for trespass and destruction of property. Who knows? It's a gamble.