I think a case can be made for your Friedrich Wilhelm being in dragoon regiment 7. In 1885 Saarbrücken was the garrison of the regiment.
Also, the photo shows what appear to be a few campaign medals on his medal bar. DR 7 fought in all three wars of unification- 1864, 1866 and 1870/71, though I am not sure I see an Iron Cross on his uniform.
Can you make out anything that is on his shoulder board??? A cipher or a number, perhaps?
I'll look through a few other sources I have, but iunformation for enlisted is very rare.
I'll let you know what I find.