Hey everyone, this si my first thread, I have an epiphone g-310 sg that after 8 years of almost daily playing it's selectror switch gave out, so went to a local store and got a new one to replace it. When i was done soldering together I noticed the ground wire to the output jack had come off, so resoldered that one and after inspecting all the wires before putting the backplate back on I realized a ground wire coming from the bridge volume knob was loose, inspected all solder spots to see if any of them seemed like it came from there but no luck, also tested connections with a multimiter and all the pots are connected to one another, but they have no connection either to the jack or to the switch, the switch do has connection to the jack, so i don't know if i should solder it to the ground side of the jack, since there's already a ground wire from the switch connected there, is it ok to have two ground cables meet at the jack? I've attached a pic of the wiring, there you can see the loose wire. That's factory wiring by the way.

Thanks in advance.
9 out of 10 of the time the switch is fine and the wiring fell apart. however I'm not a fan of the box style you see on really low end bc rich guitars and all. Why a shop will recommend a new switch is preying on the gullibility of the people to make a buck. oh yeah get the 30$ gibson one! it gives you more Hawaii .. i mean ... umm.. tone! YES TONE!

I agree with explorerbuilders reply , here's a bit more insight

essentially ground is a trail in and out of the guitar. Take any 4 pot and 3 way selector diagram and grounding is the same. From Jimmy Page wiring which is one of the most difficult les paul harnesses you'll do to obscure stuff like 4 volume and the same 3 way , pots are pots, switches are switches.

so put simply
one ground wire to the selector, as signal goes in and out of it with two wires

pot to pot making a backwards C , why the C is you dont want to over lap groundings or you'll get noise

and to the sleeve of the input jack

here's two photos to help
firstly 50s wiring ,focus on the black brush i added in photoshop

and the selector this is more straight up than the classic way it was drawn on the older seymour duncan diagrams
Thank you both, those diagrams were a huge help. Following that principle the cable should go to the jack since in any pot it would cause a loop and induce noise. As for the switch in this case it actually broke, as shown by the image, I like to check stuff myself so I know exactly what the problem is and I don't end up paying for something that wasn't needed, has happened to me many times.