I believe you can deal with these changes directly with the D trigger. You can see that the left and right changes are the same, which means that the left 3 and the right 3 are separated. You can use KL signal to control the work of three triggers to realize the above lamp changes.

If K 1=0, this can be used as a total control signal, which is connected with KL and KR through AND gates. And gate is actually a switch, K 1=0, and the gate is not conductive, K 1= 1 yes, and the gate changes according to another signal. Or you can use or door, but I see the third point. I think you can do it with the OR door,

Or the door, you can achieve your two requirements of 2 and 3.

The second requirement is very simple, that is, K 1=0, then the OR gate is more controlled by KL and KR signals. If it's all open, it's all open

The third requirement is also very simple. You can use K 1= 1 to receive the taillight signal directly. Simultaneous illumination can be realized.

There is one last question. If K2= 1, it will be lit at the frequency of 1HZ. You should design a timer to generate a signal with the frequency of 1HZ with 555, and input it directly into the taillight.

If several items need to be related, they can be solved by AND gate or OR gate, and then by latch.