I did suggest a customized Desktop background picture first up would that suffice, or is it a problem when other windows obscure the Desktop background?
If you want a narrow strip across the top of the Desktop, and if you wanted it to always be displayed at all times, then you would have to use a .jpg window, sized and positioned accordingly that loads at startup, and somehow set to be "always on top" of other windows. If you didn't want such a window to steal screen real estate from other windows then those other windows would also need to be permanently resized to a size so that any strip was always visible.
I think I would end up cheating and stick a strip of "dymo tape" across the actual plastic top of the Monitor of any such computer.