Describing the operation of a Bistable Flip Flop.
Two versions of a Bistable Flip Flop
Transistor version scroll down to Bistable Flip Flop.
IC version scroll down to 555/556 BiStable.
Wire the +12 to the circuit to the headlights dim. Not familar with the pass switch. If it runs a relay or directly to bright lights.
A small nuisance will occure not isolating the brights voltage. Not only with the BiStable Flip flop operate when pressing the passing light. It will also operate each time the brights are turned on.
To isolate a passing switch that directly connects to the brights. A heavy duty 20-30 amp Diode is spliced into the passing light swirch wire. Connecting the BiStable FlipFlop input connected on the Anode or switch side of diode.
If the passing switch operates a relay first. Is less complicated it's just wired in without a diode mod.
Notice the BiStable circuits. The trigger is a short to negative voltage or ground. An additional trasistor or a small light duty relay to convert a positive trigger voltage to a negative. Or you can use PNP trasistors in the trasistor bistable flipflop.
Goodluck if you get it to work. Make some extra ones. Encase them in epoxy and sell em for $100