Sticky residual left by labels can be easily removed with charcoal lighter fluid. Alcohol just won't cut it...
Remove the label by peeling off with your fingers or soaking in water, dampen a paper napkin or paper towel with the lighter fluid then rub on the gummy residual. KEEP AWAY FROM FLAME, for gosh sakes!
I sometimes find that I have to dampen another paper napkin or find a clean spot on the one I'm using and rub some more if the residual is excessive. But you usually find that it won't take much fluid or rubbing to get the sticky, gummy residual off the piece.
I do this with the wine bottles I up-cycle or re-pupose and paint.
My better half re-uses jars that once contained something he bought from the grocery store. He hates the paper labels.
I've purchased glasses and cups, peeled off the label from the bottoms and was left with annoying sticky stuff.