It's a nice idea, but for me it suffers straightaway as it doesn't seem to be a realistic situation - it's more like a sketch of a hospital than anything more researched. I very much doubt, for example, that a head surgeon would be going around chasing relatives or next of kin - there are nurses and admin staff to do that sort of thing. Hospitals also have policies and procedures to deal with the kind of situation described, and throwing something valuable found on a patient's person into an unsealed plastic bag in a desk drawer would not be among them - the surgeon would presumably have to call the police straightaway for that quantity of gold (same as if drugs were found, or whatever).
Of course you could just say it's a modern morality play, and it isn't intended to be at all realistic, which would be a valid viewpoint, as long as the viewers see it the same way.
So the setup is OK (apart from the above points), but then the script seems to get bogged down in detail in Act II. Do we really need to know that Kayleigh is eating a strawberry, chewing a strawberry, then swallowing a strawberry? And there is other action stuff and long-winded dialogue that probably doesn't need to be there (if you intend anybody else to evaluate this other than yourself, that is. If you're the only person who is going to be looking at the script then it's not such a problem). As it is, I reckon it's a 15-page script that takes 20 pages.
I do think it all falls apart a bit in Act III with the random shootout etc. It's a shame, as it has a lot of potential as a short film concept.
Finally, I can't help but think that "Gold Rush" would be a better title than "Gold Mine" (although I appreciate the pun in the latter).