Below is a simulation of my circuit for doing the sequence:
All lights go on when the first pulse arrives.
If it's continuous, as when braking, then all the lights stay on.
If it is the turn-signal sequence, then all lights stay for the first pulse duration and the next pulse starts the sequencer routine.
LTspice doesn't show the pinouts for the devices, or the power and ground for the logic circuits on the schematic so you will need to get those from the data sheets.
The A, B, and C outputs can directly drive grounded source N-MOSFETS, or P-MOSFETS with their sources to +12V (directly to +12V, not V+ on the schematic). The MOSFETS should be rated for 100V or more.
All capacitors should be rated for 20V or more.
Edit: R6 and C7 provide a small delay to avoid a glitch in the sequencer first output pulse.
R1 and R2 should be 1MΩ trimpots so you can adjust the time for the two 555 periods. U1 must be adjusted to have a timeout slightly longer than period of the turn-signals (the schematic is set for a 1 second period). U2 determines the sequence rate of the lights.
Make sure you add 0.1μF caps from each IC power pin to ground for proper decoupling.
Of course you need two of these circuits, one for each set of tail-lights. The 4081 has left over gates which you can share between the two circuits as well as sharing V+. Connect any unused gate
inputs to ground.
Since I haven't built the circuit, the actual circuit may operate slightly differently than the simulation shows, but I'm reasonably confident that it will work. If you built it and have any problems, post them and I'm sure we can resolve them.
Edited schematic:
View attachment Taillight Sequencer.asc