Edit: So after reading more up on 3 way switches I may think I know how they originally wired it though, I just haven't seen any diagrams done this way. It looks like they passed the 2 traveler lines through the first light and then to the second switch then the power would be coming from the second switch to the other lights. Not sure if this is accurate but maybe someone can shed some light on it as I haven't seen it done like this.
I bought a house and the basement was gutted and I'm trying to rewire the 3 way switch on the basement stairs, although I can't find any diagram that comes close to the existing wiring that is setup.
What I have is a light switch at the top of the stairs that has power coming into it. From that switch it then has a 3 wire running up to a light above the switch, which has never worked since i bought the house.
From that light at the top of the stairs there are two wires one 2-wire and one 3-wire running down to the bottom of the stairs that are both just sitting in a Junction box.
What I believe is that the junction box with the 3-wire was the secondary switch and the 2 wire was the light at the bottom of the stairs.
Here is a diagram of the current wire setup.
Blue = White Wire Green = Ground
As you can see in the diagram from the light at the top of the stairs it then has 2 wires running to 2 junction boxes at the bottom of the stairs.
I tried adding another switch to the 3-wire junction box 1 but the light at the top of the stairs still didn't work.
I can't really find any diagrams for 3-way switches that has this same wiring.
Edit: Here are some secondary pics
Here is the light above the light switch at the top of the stairs.