Hello Dennis,
Let me see if I understand correctly. There is some type of "angel eye" controller that has basically 4 conductors coming out of it? One of them is always +12V. The other three cycle through the 8 different combinations (on-off-on, on-on-on, on-on-off, etc) whenever you press a button? When you press the button though, the indicator inside the auto does not match the pattern that is shown on the outside of the car. What you want is an addition to your system that is inside the car that mimics what the actual fog lights are displaying. If it will help the collective understanding of this system, can you post a link to such a set of fog lights that might have enough description? You mentioned there are two LEDs inside the light. Based on your circuit, it seems that there should be three? Or perhaps there is one that has two elements inside it and another with only one element?
I still not 100% sure I understand this circuit, but at first glance, I am doubtful that some simple AND gates will solve your problem. In any case, an AND gate asserts its output only when both inputs are asserted. Further, if both inputs are +5, the output is +5, if both are +3, the outputs are +3 ... it does not add the input voltages.
Lets say for a moment that there are 3 outputs on your box, red, green, and blue (RGB). Each of these otuputs is +12V, it would be a fairly simple exercise to just tap each leg and connect it to your interior indicator. So that when the controller turns on the red fog light, your red interior led lights up. Is this kind of what you want?