I seem to remember horizontal surfaces in my house, as well as workshop… I see glimpses of them now and then!
I have four of those multi-drawer storage units, saved from the skip at work. Very flimsy steel pressings with brittle plastic drawers, but I nested four in a wheeled stand I made both for a Warco sheet-metal former with these storage units below. The units are lettered A to D, the drawers numbered though by the corner ones only; 1 to N in each unit.
The idea…. assuming similar longevity… Rather than individually labelling each drawer, prepare a printed, alphabetical index, using a spread-sheet and MoD-style nomenclature*, so that it's easy to locate particular items, but also to facilitate moving or changing drawers and contents. The number refers to location, not specific drawers.
* E.g., " Nuts. M6, St/Stl . Nyloc ". [Unit & Drawer] "A .15 " (1 row, 6 columns on the list)
Round Tuits, Spare Moments…. I think I had some. Now, where did I put them?