begin insult to your intelligence >" Short answer, if you have to ask, you shouldnt be doing it." End insult.
Sean, this is a safety of life application, uncertified do it yourself circuit tricks are not a good idea here, can you pull another wire? Aircraft wiring has to be designed as fail safe. The fact that the airplane is chassis ground is whats messing up any possible DC switching scheme. Plus the fact that if the wingtips fail, plus your strobes or beacons or tail fails, you risk a air to air collision.
You could build a network that would allow you to inject a audio tone onto the wire to turn on the strobes, using a simple decoder like a 567 chip.But you'd have to keep that signal out of the rest of the airframe, out of nav gear, radio gear, and anything else flight critical. You also have to choose a tone that is not used in the radios or avionics, ie not 9600 hertz,1100 hz, 1200 hz, 400 hz, 60 hz or any of the ILS marker tones etc.
A microcontroller could "catch" a momentary interuption of the DC to the lamps and toggle a flip-flop to turn on the strobes, but this is highly unlikely to be certifiable even on a home built. You'd have to shield and filter the daylights out of the microcontroller to keep its radiation of its clock signal to a minimum to keep it out of your radios. And the strobe PSUs can/will pull a nasty current ramp after every flash possibly generating a pulse that mimics your signal. Not good.
The other thing to be considered is the noise and power spikes on a aircraft DC bus are huge, especially at startup. In a car for example I've measured 500V spikes. My Cessna 172 manual (I'm considering getting a license) calls for switching off the avionics bus during engine start, even on a in flight restart. Its that bad. You'd have to protect against that.
On the other hand, the strobes are a definate plus for flight safety. FAA calls for the pilot to have the ability to your the lights off, least you end up in a cloud or fog. T
There is a guy who writes on DIY aircraft electronics and sells some kit gear, he would know of any approved alternative solution to your problem. Try rec.aviation.misc or Jim Weir @