A B737-300 FLC LANDS ON RWY 13L WHILE PRECEDING ACFT'S TAIL STILL IN THE RWY AREA AT DAL; TX.

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IT WAS LAST DAY OF 3-DAY PAIRING. WE WERE ON THE 5TH OF 6 LEGS. FATIGUE; I FEEL; WAS A FACTOR. APCH CTLR ASKED US TO KEEP OUR SPD UP. I WAS PNF; FO WAS PF. WE WERE ABOVE 220 KTS AND HIGH WHEN CLRED FOR VISUAL. AS WE HAD BEEN DISCUSSING BEST WAY TO GET DOWN TO 'THE SLOT' (500 FT AGL; SPOOLED; AND ON GS) ON PREVIOUS APCHS AND COMPARING METHODS; I ASSUMED HE WOULD BE TRYING A DIFFERENT TECHNIQUE. BUT; IN OUR APCH DSCNT CHKLIST; HE NEVER MENTIONED THAT; SO I'M NOT SURE IF THAT WAS HIS INTENT. IT MAY HAVE BEEN FATIGUE ON HIS PART. AS WE STARTED TO CONFIGURE; IT WAS APPARENT THAT OUR HIGH LNDG WT AND QUARTERING TAILWIND WERE WORKING AGAINST US. I ASKED THE TWR FOR S-TURNS AS A LAST RESORT MANEUVER PRIOR TO GOING AROUND. (AT THE TIME; I WAS CONVINCED WE WOULD.) TWR SAID 'YOU CAN HAVE RWY 13L; THAT'LL GIVE YOU AN EXTRA MI TO GET DOWN.' WE AGREED TO DO THAT. THE PROB WAS ANOTHER ACFT WAS ON SHORT FINAL AND WE WERE ENCROACHING ON HIM. IT WORKED LIKE WE WERE GOING TO MAKE THE SLOT. I HEARD TWR TELL PRECEDING ACFT; 'NO DELAY ON EXITING RWY; MAKE NEXT TURNOFF.' AT THAT POINT; I REFOCUSED ON THE TOUCHDOWN ZONE AND ENSURING WE HAD GEAR DOWN; APPROPRIATE SPD; ETC. IN THE FLARE; I LOOKED DOWNFIELD TO SEE THE OTHER ACFT'S TAIL STILL IN RWY AREA. INSTEAD OF TAKING ACTION AND INITIATING GAR; I WAITED FOR THE TWR TO INSTRUCT US TO GO AROUND. HE NEVER DID. I DON'T KNOW IF HE DIDN'T NOTICE OR JUST LEFT IT UP TO US. WE TOUCHED DOWN AND STOPPED -- WELL SHORT OF INTXN OF AFOREMENTIONED ACFT. BY NOT INSURING THE FO AND I WERE THINKING THE SAME; 'I'M GOING TO SEE IF I CAN SLOW DOWN FASTER THIS WAY;' I ALLOWED 2 OF US TO BE LEFT IN A TIGHT SIT. BY NOT TAKING ACTION WHEN I SAW THE NEED; BUT INSTEAD WAITING FOR OTHERS TO ACT; I ALLOWED A LOSS OF RWY SEPARATION TO OCCUR. THE FRIGHTENING PART WAS THE SCENARIO LEADING UP TO THE EVENT WAS ALL TOO FAMILIAR. ANOTHER B737 ACFT HAD AN ACCIDENT DOING ALMOST THE EXACT SAME THING; SMALL DIFFERENCES IN THE FINAL APCH TO TOUCHDOWN; BUT BASICALLY THE SAME. 2 PLTS; TIRED AND NOT BEING THE MASTERS OF THEIR OWN FATE. IN THE FUTURE; I WILL NOT LET FATIGUE AND COMPLACENCY SIT IN MY COCKPIT.