The previous owner of my car ('65) was attempting to do this when I bought the car. I say attempting because he never got it to actually work, I found out because he never wired correctly.
Anyways, he used (and this would work, I just chose to pull it all out) a 30A relay, using the power for the headlights (from the headlight switch to the bulbs) as the trigger circuit. On the power circuit he ran wires to the headlights and to the parking lights.
Those relays are a dime a dozen, you can get them at a good electronics store, good auto parts store, or online at partsexpress. Personally, I don't think it's worth tearing into the stock wiring to do such a mod, but if the wiring is festering anyways, go for it.
-Chris