Most stud partitions which I have come across (or even built!) have horizontal noggins between the uprights at approx 1/3 and 2/3 of ceiling height. If yours is like this, you'll need to get through both the upper frame member (no problem from above the ceiling) *and* the noggin at 2/3 height. This is the fun bit! Unless you remove some of the plasterboard, you will need a very long, thin drill - well it can be 1/2" dia, but needs to be upwards of 3' long. The cutout for the switch is easy - and you can use a hollow-fixing box. It will help if your holes through the top frame and noggin are in line with the switch. You will then need a long piece of stiff wire, fed down through the holes, and retrieved through the switch cutout, to pull the cable through.
HTH, Roger