I don't want to jump in and take anyone’s thunder but my answer would be yes as I think Bill K was getting to when he asked the question.
Based on the fact of separate switches for each light type then there should be separate wiring to the lights for each one.
I would tap off of the wiring to the headlights or parking lights wiring with a low-amperage fused line to a relay and use the relay to control the main power to the lights.
Use two relays and properly sized fused power lines from the battery to the relay and then to the lights, that should handle it.
The trick is to find the control power that you want; high or low beams, parking lights or what ever.
Take your time find the correct wires, double check which wire is what and make good soldered connections and use heat shrink (w/glue in it).
Don't forget to clean the soldered joint with alcohol.
One more thing, maybe a good idea to run a switch in the wire from the relay control power to each relay; just in case you decide you want to shut them off OR you may want to consider a separate circuit to turn the lights on separately ????
