B737-300 CREW EXITED THE RWY AT THE LIGHTED HIGH SPD TURNOFF; ONTO A CLOSED AND BARRICADED TXWY AT JAX.

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AFTER LNDG ON RWY 7; WAS INSTRUCTED TO TURN OFF ON TXWY F. I MISTOOK TXWY G (WITH LIGHTED HIGH SPD TURN OFF GREEN CTRLINE LIGHTS ILLUMINATED) FOR TXWY F. AFTER EXITING THE RWY ONTO TXWY G I WAS LOOKING DIRECTLY INTO VERY BRIGHT WORK LIGHTS BEING USED BY WORK CREW ON XING TXWY A. THE LIGHTS WERE SO BRIGHT AS TO NEARLY OBSCURE BARRICADES AT TXWY A ON TXWY G. THERE WAS ROOM ON THE OPEN PORTION OF THE TXWY TO CLR THE RWY AND BARELY ENOUGH ROOM TO REVERSE COURSE LATER TO RETURN TO RWY 7 AND TAXI DOWN RWY 7 (WITH TWR CLRNC) TO TXWY F FOR TAXI TO GATE. THERE ARE NO NOTAMS LISTED IN CHART MANUAL NOR ON FLT RELEASE PERTAINING TO THE TXWY CLOSURE. IF THE CLOSURE WAS ON THE AUDIO ATIS; WE MISSED ITS MENTION. THERE IS NO DIGITAL ATIS (FOR ACARS RETRIEVAL) AVAILABLE AT JAX. I FELT SOME PRESSURE TO CLR THE ACTIVE RWY DUE TO TFC FOLLOWING ON APCH AND HAD NO REASON TO BELIEVE THAT LIGHTED HIGH SPD TURN OFF 'LEAD-IN' LIGHTS WOULD BE ON A 'CLOSED' TXWY. PLUS WORKERS HIGH INTENSITY LIGHTS POINTING TOWARD RWY MOSTLY OBSCURED BARRICADES; WHICH WOULD HAVE FURTHER CLUED ME TO THE FACT THAT I COULD NOT PROCEED TO THE TERMINAL VIA THIS TXWY. SUPPLEMENTAL INFO FROM ACN 599345: AFTER LNDG ON RWY 7 AT JAX; WE ATTEMPTED TO TURN OFF THE RWY ON TO A TXWY THAT HAD LIGHTED LEAD-OFF LIGHTS. THE TWR HAD TOLD US TO TURN ON TXWY F; WHICH WE THOUGHT THIS WAS. HOWEVER; DUE TO A CONTRACTOR PAINTING CREW WORKING ON THE PARALLEL TXWY AND HAVING A VERY BRIGHT WORK LIGHT SHINING RIGHT AT THE RWY AND TURNOFF; WE WERE NOT ABLE TO SEE THE TXWY IDENT SIGN OR THE CONES BLOCKING THE TXWY AT THE JUNCTURE WITH THE PARALLEL UNTIL WE WERE WELL INTO THE TURN. WE STOPPED THE ACFT CLR OF THE RWY AND SHORT OF THE BLOCKED TXWY; AND THEN RECEIVED CLRNC FROM THE TWR TO REENTER THE RWY AND PROCEED DOWN TO THE NEXT TXWY. MY OBSERVATIONS ON THIS INCIDENT ARE AS FOLLOWS: IF THE TXWY CLOSURE WAS ON THE VOICE ATIS (JAX DOES NOT HAVE ACARS ATIS) WE MISSED IT. ALL ARPTS SERVING ACR ACFT SHOULD HAVE DIGITAL ATIS FOR BOTH DEP AND ARR. IT IS MUCH EASIER TO MISS ITEMS ON A LONG VOICE ATIS. THE LEAD-OFF LIGHTS SHOULD NEVER BE LIT FOR A CLOSED TXWY. THIS TYPE OF ERROR CONTINUES TO LEAD TO PROBS ON ARPTS AT NIGHT; AND I AM AMAZED THAT ARPT OPS WILL STILL DO THIS. CONTRACTORS SHOULD NOT BE PERMITTED TO POS THEIR WORK LIGHTS SO THAT THEY ARE SHINING DIRECTLY AT A RWY OR DOWN A TXWY. THIS WORK LIGHT WAS POSITIONED DIRECTLY IN LINE WITH THE TURNOFF. UNLIGHTED CONES OR BARRIERS AT NIGHT ARE NOT ENOUGH TO MARK A CLOSED TXWY. IF THESE WERE LIT WE WERE NOT ABLE TO SEE THEM BECAUSE OF THE BRIGHT WORK LIGHT.