Oh, okay, now I know what we are talking about. Something like this, correct?
**broken link removed**
Can you open one up and peek at how the tube is triggered? Any chance of modifying that circuit? Its possibly all SMD components or potted and if thats the case messing with it isn't going to be a good idea. If you can modify it, you may be able to control the trigger on the flashtube and not have to switch the line voltage on and off.
If you don't mind a relay cluncking away, it would be pretty simple to alternate power between the 2 lights. If you can find a relay with both NO (normally open) and NC (normally closed) contacts, you can use something like the classic 555 timer astable circuit to open and close the relay. With one light on the NO and the other on the NC contacts, when one is on, the other will be off.
Do some reading on strobe circuits and the 555 timer, relays, ect and post back if you have questions.
If you do open the lights and mess with them, be extreamly careful. Strobe lights use high voltage to operate and can give deadly shocks. Even with the power removed, the capacitors can hold a sizeable charge for quite a while.
Edit - just re-read your first post. So are these going on a car or truck? You mention 12/24v but then said they are from a building. Are they 12/24v AC or DC? I would lean toward them being AC if they are from a building. If they are AC, they won't work in a car.