TURBOPROP FLIGHT CREW RECEIVE GPWS TERRAIN WARNING WHILE TRACKING THE JST ILS 33 LOCALIZER AT 4000 FT MSL AS CLEARED BY ATC.

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INBOUND TO JST AIRPORT FOR THE ILS 33; CLEVELAND INSTRUCTED US TO TURN LEFT AND DESCEND TO 4000 FT AND INTERCEPT THE LOCALIZER FOR RUNWAY 33. THE PILOT NOT FLYING READ BACK 4000 FT TO ATC ALONG WITH THE REST OF THE INSTRUCTIONS; SET 4000 FT IN THE ALTITUDE WINDOW AND STATED 4000 FT TO THE PILOT FLYING. THE PILOT FLYING VERIFIED 4000 FT IN THE WINDOW AND READ IT BACK TO THE PILOT NOT FLYING AND WE BEGAN OUR DESCENT. THIS WAS A CLEARANCE WHICH PROVIDED US AMPLE TIME TO TRACK THE LOCALIZER INBOUND; ONCE ESTABLISHED; FOR QUITE A WHILE. WE HAD REMARKED THAT 4000 FT WAS LOWER THAN THE PUBLISHED GLIDE SLOPE INTERCEPT ALTITUDE AND WE CONFIRMED AGAIN WITH PILOT FLYING AND PILOT NOT FLYING THAT OUR ASSIGNED ALTITUDE WAS IN FACT 4000 FT. WE DID NOT CONFIRM IT WITH ZOB BECAUSE: 1) WE WERE STILL IN CONTACT WITH THEM AND FIGURED THIS WAS JUST A LOWER ALTITUDE TO INTERCEPT THE GLIDE SLOPE THAT WOULD STILL BE ABOVE THEIR MVA FOR THE APPROACH; 2) WE WERE VMC AND HAD THE RUNWAY IN SIGHT; AND 3) WE HAD BEEN FLYING AT THIS ALTITUDE FOR QUITE A WHILE ALREADY WITHOUT A REMARK ABOUT IT FROM CENTER. ZOB THEN CLEARED US FOR THE APPROACH AND TOLD US TO CONTACT JST TOWER. MOMENTS AFTER CONTACTING JST TOWER; WE GOT A GPWS TERRAIN WARNING WHILE STILL LEVELED AT 4000 FT INBOUND ON THE LOCALIZER. WE IMMEDIATELY EXECUTED THE GPWS TERRAIN MANEUVER. THROUGHOUT THE APPROACH AND THE MANEUVER; WE WERE VMC AND ALSO HAD THE RUNWAY IN SIGHT. WE ADVISED JST TOWER THAT WE COMPLIED WITH A TERRAIN WARNING AND CLIMBED AND WERE NOW AT 4600 FT; TO WHICH THEY REPLIED 'ROGER; STATE YOUR INTENTIONS.' SINCE AT THAT TIME WE WERE ALREADY AT THE PUBLISHED ALTITUDE AND STILL HAD THE RUNWAY IN SIGHT; WE TOLD JST TOWER THAT WE WOULD STAY AT 4600 FT AND INTERCEPT THE GLIDE SLOPE FROM THAT ALTITUDE IF THAT WAS OK WITH THEM. THEY SAID NO PROBLEM. WE THEN CONTINUED THE APPROACH AND LANDED ON RUNWAY 33 WITHOUT ANY OTHER FURTHER EVENT.