AT 2003 CDT, THE FLT WAS CLEARED FOR AN ILS LOCALIZER APCH TO RWY 36 AT THE HARRISON/BOON COUNTY ARPT. ABOUT 7 MIN LATER, THE AIRCREW REPORTED MAKING A MISSED APCH & THE FLT WAS CLEARED TO THE OUTER COMPASS LOCATOR FOR ANOTHER APCH. THE CREW ASKED THE HARRISON FSS SPECIALIST TO INCREASE THE INTENSITY OF THE APCH LIGHTS BECAUSE THEY DID NOT SEE THE ARPT UNTIL MID-FIELD; THE SPECIALIST COMPLIED. AT ABOUT 2015 CST, THE AIRCREW REPORTED INBOUND AT THE BAKKY INTERSECTION (OUTER MARKER). THE OUTER MARKER WAS LOCATED 4.7 MI SOUTH OF THE I-HRO LOCALIZER DME ON AN OUT BOUND HEADING OF 179 GEG. WHEN THE FLT DID NOT ARRIVE, A SEARCH WAS INITIATED. THE WRECKAGE WAS FOUND WHERE THE ACFT COLLIDED WITH A MOUNTAIN AT THE 1840' LEVEL ON A HDG OF 335 DEG, 3.5 MI WSW OF THE ARPT. THE CRASH SITE WAS ALSO LOCATED ALONG THE 179 DEG RADIAL OF THE HARRISON VOR, ROUGHLY THE SAME DISTANCE & DIRECTION FROM THE VOR AS THE OUTER MARKER WAS FROM THE LOCALIZER DME. THE ARPT WX WAS 500' OVERCAST, 2 MI VISIBILITY WITH FOG. ARPT ELEVATION - 1364' MSL.