A wall mount that fits a typical magnifying lamp with a 0.5 in. / 12.7 mm mounting post that is 1.5 in. / 38.1 mm long.

I included two versions, one that is tilted away from the wall 30° (as shown in the photos), and one that is straight up and down. This second version is untested.

When folded, my wall lamp leans backward 30° so the tilted version is what I first designed and what is shown in photos. With this version, you may need to use a screw to keep the post from rotating, as the lamp will want to swing downward. The hole for the set screw is ~ 1/4 in. and ready for a 5/16 in. -18 tap or another size insert if desired. This may not be needed in the vertical (0°) version.

Overall dimensions: 4 in. tall x 2 in. deep x 1.5 in. wide