Divide the current 10 minute average wind speed by 12. That gives the approximate wind run in miles for 5 minutes.
Estimate the current average wind direction.
Take the weather station that direction and that distance and set it down.
When the station gets wet, it'll rain at the original location in about 5 minutes.
Seriously, I don't know of anything a PWS can do with the granularity required for that kind of prediction. Around here (central California coast), I've noticed that in classic winter storms, (our rainy season), the barometer drops and drops, and it's windy. The rain generally doesn't start until the baro bottoms out and the wind dies down.
But trying to predict rain from those 2 observances is going to be pretty hard. I can get a better idea from looking at radar, or other close by stations if the rainfall is hard enough.
If it's really important, I'd consider a more elegant solution to what I described above. Figure out the prevailing directions that the storm comes from, and the average speed at which they travel.
Put one of those Hydreon RG-11 Optical Rain Gauges at the calculated location, set to the most sensitive "It's raining" setting, and use the relay contacts to signal you some how.