It seems like the most straight forward thing to do would be to connect to the signals driving the lights themselves. They are easy to find (for example you can pick up all of them at the housing for the rear lights, most can come out of one side and then you'd pick up the other one from the other side. Or you could find all of the signals together in the dash. I think the choice depends a lot on where you want to locate the Pi.
I would be inclined to use an optoisolator to protect the Pi from the vagaries of the car's electrical system and to match levels with the Pi's inputs.
If the lights are being controlled by a PWM (pulse width modulation) signal from a CAN controller (as @spicetraders suggested in the comment) – which seems like a serious case of overkill, but perhaps it is a tradeoff in terms of the number of wires that have to be run and the ability to do diagnostics against the cost and complexity of the CAN/PWM approach – you might find it easier to try and pick up the signals at the dash before they reach the various controllers. Or, perhaps we have already reached the point where everything is mediated by a controller…