THE NON-INSTRUMENT RATED PLT DEPARTED IMPERIAL, CA, AT 2010 PDT, & SHORTLY THEREAFTER, WAS IDENTIFIED & FOLLOWED BY A U.S. CUSTOMS SPECIAL MISSION ACFT. THE ACFT WAS FOLLOWED TO DEMMING, NM. DURING THAT PORTION OF THE FLT, ITS ALTITUDE VARIED FROM ABOUT 500 FT AGL TO 16,000 FT MSL. AT ONE POINT DURING THE FLT, THE ACFT WAS FLOWN AT NEAR THE STALL SPEED. WHILE EN ROUTE, THE PLT FLEW IN & OUT OFF THE CLOUDS. WHEN HE ARRIVED OVER DEMMING, HE MADE TWO 360 DEG TURNS & WAS OBSERVED IN A DESCENDING SPIRAL THRU 9000 FT. THE ACFT CONTINUED FLYING UNTIL IT IMPACTED A 5200 FT MOUNTAINABOUT 23 MI EAST OF COLUMBUS, NM AT AN ELEVATION OF APRX 4750 FT. IMPACT OCCURRED IN STRAIGHT & LEVEL FLT. AN EXAM OF THE WRECKAGE REVEALED NO EVIDENCE OF A PREIMPACT, MECHANICAL PROBLEM. APRX 40 MI ESE AT EL PASO, TX, THE 0248 MDT WX WAS: 800 FT SCATTERED, 3300 FT BROKEN, VISIBILITY 7 MI (ELEVATION 3956 FT). THE AREA FORECAST CALLED FOR SCATTERED THUNDERSTORMS & RAIN SHOWERS WITH MOUNTAINS OCCASIONALLY OBSCURED.