Wiring existing 3 Way Switch in basement stairs that was cut

Question

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.

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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

This is of the light switch at the top of the stairs.

Here is the light above the light switch at the top of the stairs.

Answer 1

Maybe the reason J Box 1 and J Box 2 were empty is that the previous owner gave up trying to get it to work. If so, this would indicate the problem is in the cables.

If J Box 2 is in a position where a light would be installed, then the circuit was most likely originally intended to be wired like this:

(Put black tape or black paint on the ends of the white wire in the 3-wire cable to indicate that it has been re-purposed as a switched hot.)

If you wire it like this and it doesn't work, then there is probably something wrong with the 3-wire cable, Disconnect everything from the 3-wire and test all the wires for continuity. Make sure all the wire-nut connections are tight - this is where I have the most trouble in my house.

Answer 2

OK here's what I see.

Imagine Junction box 2 did not exist. Go back into in Paint, select the white brush and remove everything relating to Junction box 2 including the 3 wires. That looks like a common two-switch configuration using two 3-way switches and the lamp in the middle. You should have found that on any of your web searches. Black and red are the messengers, and the white from junction box 1 is the not neutral, but switched "hot" (which should be marked as such with a band of black electrical tape near each end, but nevermind that) coming back from the farther switch to the lamp. The white from the first switch to the lamp is the actual neutral.

So far, this is totally textbook (if you ignore junction box 2 and its connecting wires).

Now imagine you'd like to put a second lamp, in a second location, that switches on and off with the first lamp. What are you going to do? Go to the first lamp's location, and tie into ground, neutral, and the switched "hot" to the first lamp. That is exactly what junction box 2 is doing. It is intended for a second lamp.