There a map in Copper Mining in Middleton Tyas by T R Horshaw that shows a level about 500 yards west of Trindalls House (now Thorndale Stud)
Only problem is that would be just to the East of Melsonby and its south of Waterfall Beck, close but not the location you mention.
It talks very briefly about this level (S-T-U) of the Duchess of Northumberlands land.
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I think that is on the other side of the road from the houses at middle caves close to the council depot