Light socket feed off a switch?

I have a small area under my stairs with no light. We put our coats and shoes in there, but without a light it is very frustrating.

On the outside wall of the space I have a light switch for the staircase. Could I connect a light to this? The light switch would only be abut 2-3" from the new light socket.

I bought a light socket with a pull cord for on/off, so the light switch would not control the new light socket.

It seems so easy to do, but is it practical or safe? I'm in Texas, 110v.

I think this will get moved to the Electrics "Abroad section". how many cables are in the light switch first?

Thanks for the quick reply!

I expect two from experience, though I haven't opened the light switch up yet.