First of all, oil doesn’t do much for this kind of gear, you want grease, preferably red, but black might do it. Vaseline will also work.
You need to disassemble the tuner by removing the screw and gear from the tuning post. Clean any old or hardened grease (with a solvent, acetone or naphtha) from the underside of the gear, the washer, plate and post, and re-lubricate with fresh grease.
You can also polish the underside of the gear with some 1200 grit sandpaper. It might help to polish the washer, too.
If you go through the trouble of removing the gear, you can also see if the stem turns freely in the bracket without any tension from the gear. Sometimes the bracket is just too tight! How does this happen? It can be because the parts are plated- if the plating is too thick on both parts, that is enough to make it tight. I could also be that the bracket was simply stamped too shallow (by a couple of thousandths of an inch), making the fit too tight. You can try to address this, but it’s a little fiddly. Sometimes, it’s just hardened grease, and a quick dip in acetone can loosen/dissolve it. It will need to be lubed again as well, and for this you could use oil, but thinned grease is still better.
If you clean, lube, and spin the stem and bracket repeatedly and it is still too tight, you can flow in some fine grit lapping or Clover compound, (4-600 grit) mixed with very light (sewing machine) oil. At this point, you may want to screw the plate to a board or the bench, and rotate the stem with a power winder a few dozen times. You don’t want to make a mess of the headstock. That should loosen it a bit more, then you can rinse the plate with solvent and re-lube…
If all this is too much, just replace the darn thing!
