Sounds like something is not properly hitting ground or you have a lead wire very close to the ground causing interference, like they are almost touching. Make sure you didnt accidentally touch a bit of ground to lead, which is what comes to mind with humbucker making excess noise.
I mounted one forever ago and had issues like this, checked, and found one of the mounting screws went through the braid and was pressing ground and lead together a bit. Whoops!
Also, there are debates on the quietest tele setups, due to the metal control plate.
I use the control plate as a shared ground, like with an LP metal plate, and do no run *extra* grounds between pots. This pulled the noise down on tele a bit.
Running an extra ground to the body will reduce ambient noise.
I hate to be this guy but.....I also test and install caps in a specific, quietest operational direction.
Heatshrinking caps and the lead and ground on the jack will also reduce background noise.