The switch looks like it achieves its modes through a resistor network that you can see on the opposite side of the switch.
Actually, I think that the modes are via 3 PT4115 PWM buck ICs. Is that driver board basically running 3 separate PT4115s, each with its own sense resistor network to set the output current? I think that might be how you get your 3 modes -- three PT4115s, three inductors, three pairs of diodes, three caps, three pairs of sense resistors (each with what looks like slightly different values to give different output currents, and each pair connected in parallel). Also, three pairs of output wires -- white/yellow, blue/green, and red/black.
That's a brute force method to implement 3 modes.
In fact, for sense resistor pairs at R1 and R2, it looks fairly clear that they connect to Pin 4 of their respective PT4115 ICs. That pin is the current sense pin. At R2, I see R33/R27. Can't read one of the resistors at R1. What is the marking on the one with the white dot on it? The visible resistor at R1 is R27. The third pair is only partially visible. I can see one marked R22. The red wire blocks the other.
Sense resistor network R2 should give nominally 667mA out. My guess is that R1 gives Low, R2 Medium, and R3 High mode.
The board also needs power. Where is Vin (Batt+) connected to the board? The two unconnected solder blobs at the two corners of the board on the end with the 3 pairs of colored wires seem odd. Are you sure that a wire didn't get broken off from one or both of those solder blobs? In fact, if you look at the traces on the board, the solder blob next to the black wire runs to Pin 2 of one of your PT4115 ICs. That pin is GND. Possibly, the other solder blob is for Vin. Or the black wire at the switch end is Vin (not GND) and the color code choice for the wire was poorly done. Where does that black wire go? Does it connect to the flashlight body, to some other switch, to Batt+, something else?
Can you take another photo of the component side, this time showing the complete board? Your photos above cut off part of the board. What flashlight is this? How many LEDs? What type -- Cree XR-E, Seoul P4, MC-E, P7,...? It would also help to get a complete picture of the system. Photos up the bore of the light at each end of the driver board might help in terms of understanding what wires are going where.