Simple on and off switch to toggle between two circuit (headlight high or low)
If we use a timing diagram to describe your requirements it becomes a lot clearer.
               ____      ____      ____      ____      ____      
Switch    ____|    |____|    |____|    |____|    |____|    |_____
               ____                ____                ____
High beam ____|    |______________|    |______________|    |_____
                         ____                ____
Dip beam _______________|    |______________|    |_______________




simulate this circuit &ndash; Schematic created using CircuitLab
Figure 2. Implementation using a bi-stable latching relay.
A bi-stable latching relay would be a simple solution.

Figure 3. Go to HomoFaciens and click &quot;Start animation&quot; to see how the pawl mechanism is advanced on every impulse of the relay coil.
The relay shown in Figure 3 will be a low current device so typically we would use that to drive a heavier duty relay to control the lights. I have not shown the additional relay in Figure 2.
If this circuit is for a car it seems like a very poor idea as the lights will go off during every transition from low to high and back again.