If all you want is a left - right pattern and don't want to be able to do double flashes, you could simply use a SPDT relay. One headlight would be connected to the Normally Open (NO) contact and the other to the Normally Closed (NC) contact. Your 12v supply would be the common.
Somthing easy like a 555 timer in astable mode could control the speed and duty cycle.
A 555 won't be able to supply enough current to operate much of a relay. But it can operate a transistor that can control the coil of the relay.
When you operate a relay coil via a transistor, you need to add a freewheel diode to protect the transistor when the coil de-energizes.
I always add this when people ask about such circuits - Flashing headlights on public roads are illegal in most places unless you are a volenteer firefighter or medic, and even then you normally need a permit. Please check your local laws.