Humming LP1 and pickups don't work individually

[ConorB]

Hi, I have just made my Les paul and Ive found that both pickups are humming and when i switch from treble to rhythm and tap the pickups both make a sound through the amp when I tap either. Is this a wiring probem?

I havent strung it or anything yet

[McCreed]

Hi ConorB.

re: humming; Probably a ground (earth) issue. Did you run a wire from one of the bridge posts to a common ground?

As for the switching problem, yes, most likely a wiring problem. (could also be related to the ground problem)
Post a (clear) pic here of your control cavity and switch cavity so we can see the pots & switch wiring and it will be easier for us to diagnose.