Check the chair inset for all loose, damaged or missing tiles.
Remove damaged or loose tile with a pair of tweezers. Be careful to hold the tile with little pressure if the inset is antique. The tiles may break easily if the tweezers are squeezed too tightly. Set the tile to the side.
Pour a capful of mineral spirits onto a rag or cotton swab. If the tile area is small, use the cotton swab to prevent loosening other tiles with excess mineral spirits. Rub the exposed adhesive with the mineral spirits to dissolve the glue. If the adhesive is difficult to remove, use a flat screwdriver to scrape the excess off the wood.
Add new tile adhesive to the wood in the empty tile space with a paintbrush.
Replace the tile in its original space, holding it gently with the tweezers. Press down on the tile with the tip of your finger to even it with the other tiles. Allow the tile to set for three hours.
Fill the spaces around the tiles with grout and press the grout into the areas until it is even with the surface of the tiles, using a grout float. Allow the grout to set for 24 hours.
Paint glaze on the tile inset with a paintbrush, covering the tiles and grout evenly. Allow the glaze to dry for 48 hours before using the chair. The glaze helps preserve the tiled chair inset for constant use.