Control dual color LED without microcontroller
I don't know what your specific restrictions are regarding space, but you should have something active. You can use a couple of gates from an inverter chip like the CD40106B, which can easily accommodate 12V.







simulate this circuit &ndash; Schematic created using CircuitLab

The inverter chosen really depends on the current of the LEDs. If you measure the current to be high, you can use an H-bridge chip or discrete transistors.