Having thought more about the shaft being sunk in the tintype image.
It looks like the picture was staged, probably for a company prospectus or an annual report. I like the way each man came to work, dressed in his best, to stand still in his place during the long plate exposure. That is typical of early engineering photographs, where a mechanic demonstrates the use of a tool, while wearing a coat and tails.
A wire cable can be seen coming out through the building wall, then passing over the large diameter wheel at the top of the headgear, to raise and lower the barrel loaded with spoil. The two cross-braced legs that go from the top of the headgear towards the winch building, counter the tension in that cable. The building must house a steam-powered drum winch, hence the tall chimney, needed to draw the heat from the firebox, through the boiler tubes.
The permanent nature of the building, housing a steam powered winch, suggests it was not a water well, nor an early oil well. This vertical shaft is planned to be used for some significant time to extract proven reserves of a mineral. The probability is that it is a new access shaft to an existing coal mine that is being extended. The shaft reduces horizontal underground transport, increases ventilation, and provides a possible escape route for survivors.
There is similar headgear shown here, out of use by the time this picture was taken, but originally constructed at about the same time as the OP tintype image.
https://www.suttonbeauty.org.uk/suttonhistory/mineworking/
View attachment 350912
The barrel shown in the tintype image was used to remove spoil, while the shaft-sinkers rode the barrel, standing on the rim while holding the wire. That dangerous practice is illustrated several times in a 678 page book, a 50 Mbyte download from archive.org;
"Underground life" : or, Mines and miners. 1869.
By Simonin, Louis, 1830-1886; Bristow, Henry W. (Henry William), 1817-1889.
https://ia903105.us.archive.org/13/items/undergroundlifeo00simo/undergroundlifeo00simo.pdf