Yes, I think the "hazard circuit" or running lights circuit would be fine. Ideally, I'd like to avoid having multiple relays involved (as John points out), and I think that would be the case if I tapped into the wires that actually connect to the bulbs.
If I could simply provide power (through the alarm) to one wire (in parallel with the hazard switch? or running lights switch?), and let the car's wiring/circuitry do the rest of the work for me, that would be great.