WW24 CAPT ENTERS RWY AT GJT WITHOUT CLRNC AS ACFT LANDS ON OPPOSITE END OF RWY.

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PROB AROSE WHEN I TAXIED ONTO AN ACTIVE RWY. I DISCOVERED THIS WHEN I SAW THE LNDG LIGHTS OF AN ACFT ON LNDG ROLLOUT; ON THE RWY AT THE OPPOSITE END. THEY HAD LANDED ON RWY 11. I HAD TAXIED ONTO RWY 29. CORRECTIVE ACTION: AS SOON AS I SAW THE LNDG LIGHTS; I REALIZED WHAT I HAD DONE AND STARTED A 180 DEG TURN TO EXIT THE RWY. AT THE SAME TIME TWR CALLED AND SAID TO TAXI CLR OF THE RWY. CONTRIBUTING FACTORS: EARLY MORNING TKOF FROM HOUSTON; TX; CLR SKIES AT DEST; CALM WINDS; NO TFC. SUNDAY MORNING AT XA40. A HUGE FACTOR WAS THAT OPS WERE BEING CONDUCTED IN BOTH DIRECTIONS ON RWY 11/29. I LANDED ON RWY 29. THE ACR LANDED ON RWY 11. WE WERE HOLDING SHORT OF RWY 29. WE WERE ANTICIPATING TKOF CLRNC. TWR CALLED AND SAID TO FLY THE XXXX DEP AND CLB TO XXXX FT. I KNOW BETTER; BUT I UNDERSTOOD THIS AS TKOF CLRNC; AND STARTED TO TAXI ONTO THE RWY. TWR AND GND WERE COMBINED. WE HAD CALLED THE TWR TO CLARIFY TKOF CLRNC AND RECEIVED NO RESPONSE. WE CALLED A SECOND TIME; WITH NO RESPONSE; THEN I SAW THE LNDG LIGHTS. I AM NOT SURE IF THE OTHER ACFT HAD ALREADY LANDED AND WAS ROLLING OUT WHEN WE WERE CALLING THE TWR; BUT I THINK IT WAS ALREADY ON THE RWY. HUMAN FACTORS: FATIGUE FROM A HVY SCHEDULE THE PREVIOUS WK; EARLY MORNING WAKE-UP AND DEP. PERCEPTIONS: I HAD EXPECTED A TKOF CLRNC. INACTIONS: I WAS TOO COMPLACENT. I WAS RUSHING TO GET BACK TO HOUSTON SO I COULD CALL AND CHK ON A PATIENT'S HEALTH. I DID NOT STOP TAXIING WHEN I DID NOT RECEIVE A RESPONSE FROM THE TWR. I DID NOT CONFER WITH MY CO-PLT. I DID NOT STOP BEFORE IT WAS TOO LATE. SUPPLEMENTAL INFO FROM ACN 615446: INSTRUCTIONS WERE REPEATED AND MY CAPT REPEATED CLRED FOR TKOF. THIS IS WHAT HE BELIEVED HE HEARD. I WAS WORKING ON CALLING OUT THE BEFORE TKOF CHKLIST AND CANNOT HONESTLY REMEMBER IF WE WERE EVER CLRED FOR TKOF. HOWEVER; THE CTLR NEVER CORRECTED THE READBACK. WE NOTICED ANOTHER ACFT WAS ON SHORT FINAL FOR THE OPPOSITE RWY. WE IMMEDIATELY EXITED THE RWY.