A Leathery pulse is specific to examination between the superficial and moderate levels. The Leathery pulse demonstrates a leakage of Qi or the inability of Qi to move upward. It shows a significant underlying deficiency complicated by a great effort to appear strong.
Leathery pulses can also mean that there is some type of stagnation at either the Blood (moderate) level or in the Yuan (deep) level preventing the patient from having full resolution of their imbalance. The origin, of course, will be some kind of Qi and/or Blood stagnation responding to the deficiency of a medium, but the visual appearance of the patient will often not betray that deficiency. You won’t know it until you examine the pulse and find that belying the appearance of the patient is a significant deficiency. I think of this as being like a physical stoicism.