The cable coming from the left is from the fuse box, it's 12/3 (aluminum). The cable going straight down is going to a switch (it's 12/2, aluminum). The other cable going down and curving slightly to the right is going to a light fixture (14/2 copper). The cable going up is also going to a light fixture (14/2 copper). The cable going to the right is carrying power to another room (12/2 aluminum).
So there's essentially one X/3 coming in, and four X/2 going out. The aluminum to copper needs to be property pigtailed with a purple wire nut (which is accepted here). Let's ignore that issue for now; I'm trying to understand if my assumptions about this setup are correct and why it might have been set up this way.
When I open the switch, the lights turn off, as expected, and voltage drops to 0 on the red wire (R) coming from the fuse box. The black wire going to the other room remains live.
When I close the switch, the lights turn back on, and there is now 120 volts on the red wire (R) going to the fuse box. The wires going to the other room remain live, of course.
Now, I'm assuming that the 12/3 cable is the one delivering power to this circuit, and is coming from the fuse box. The white wire is shared common for the lights and the other room. Which makes it seem like the red wire is useless. Does this seem correct?
To me, it seems the 14/2 wires were retrofitted into this box to add additional lights, and originally this junction box was the one that had a light attached to it. Which makes me think that the red wire from the fuse box should be used as the neutral/return for the lights; so the lights and the other room both share power from the same black from the 12/3, but return power on the other two wires, separate from each other.