We used some duct tape to hold the tiles in place on a vertical surface, now we need to clean the residue without scratching the glazed surface.

I tried using acetone nail polish remover, but it dries too rapidly. Any suggestions?

https://www.abanet.org/soloseznet/threads/0511/ducttape.html

The above link seems to have a lot of suggestions, but try to test first on scrap piece if you can.

It's true that acetone will dry too quickly.

A rag soaked with hot water and dish soap while using a single-edged razor blade will work in a short amount of time. Depending on how large an area that you need to clean, and if the residue might be within textured portions of the tiles if they are textured then you may need to use chemicals. If you need to use chemicals, then I would suggest Goof-off or Oops! Both or one or the other should be available at most paint and hardware stores. Another thing to use would be lacquer thinner.

I would try to avoid using any chemicals just for health reasons, though. The rag soaked with hot water and dish soap while using a single-edged razor blade should work just fine if the tiles are perfectly smooth.

Please be sure to read the instructions on the labels, use rubber gloves, where goggles if doing a large area and have adequate ventilation, if you plan to use any chemicals.

Try some liquid cooking oil, perfectly safe, won't dry up, and has a strong cutting action. You can even wipe it on and come back in a while after it has softened stuff up.