What is the etymology of "pan out"?

pan ( v) (Online Etymology Dictionary):

"to wash gravel or sand in a pan in search of gold," 1839, from pan (n.); thus to pan out "turn out, succeed" (1868) is a figurative use of this (literal sense from 1849).

pan out

1. pan out - be a success; "The idea panned out": bring home the bacon, deliver the goods, succeed, win, come through - attain success or reach a desired goal
2. pan out - wash dirt in a pan to separate out the precious minerals pan off, pan wash - separate dirt or gravel from (precious minerals)

(Thesaurus based on WordNet 3.0)

out (particle)

12. used to indicate exhaustion or extinction: the sugar's run out; put the light out.

(Collins)

Here's an example of (12), from family descriptions I've heard of soil fertility in the Deep South:

Those fields were cottoned out.

It means that from so many years of growing cotton, without enriching or resting the soil, the soil was fertility destroyed or damaged.

In a similar way, I could imagine someone saying that a mine or a region was panned out, meaning that gold had been panned to such an extent there that there was no significant gold left available there.