In the hall wall closet it needs light. There is no electric outlet close by that I can tap into. Only a switch nearby. Can I tap into a switch.
The switch only has a positive wire. No neutral.

Is this correct??

Yes you are correct, if the switch has only one romex cable in the box. That will not help. Are there any opposite walls to the closet that have an outlet adjacent the closet? Check to see if they are duplex or switch with a neutral.
Qu. Is there any access space above in the ceiling? nmwirez