ACR LTT STARTED TURN ON WRONG RWY AT TRIPLE INTERSECTION OF 2 RWYS AND TXWY AT GGG.

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ACFT WAS CLRED TO TAXI TO RWY 17 VIA HOTEL. GND ADVISED THAT 4100' REMAINED AT HOTEL FOR RWY 17. INITIALLY WE ACCEPTED THE REDUCED LENGTH; BUT WHILE HOLDING FOR TKOF CLRNC WE CHANGED OUR MINDS AND REQUESTED THE FULL LENGTH RWY 17 FOR TKOF. TWR THEN CLRED US TO BACKTAXI AND HOLD ON RWY 17. I INADVERTENTLY TAXIED ONTO RWY 13 AND PROCEEDED TO BACKTAXI. TWR INFORMED US OF OUR ERROR AND ASKED US TO EXPEDITE CLRING RWY 13 AS TFC WAS ON 3 MI FINAL FOR 13. WE COMPLIED AND TO OUR KNOWLEDGE ALL OTHER OPS PROCEEDED NORMALLY. TXWY HOTEL IS AT THE INTXN OF RWYS 13 AND 17. IF THE PLT IS NOT INFORMED OR IS DISTRACTED; IT IS VERY EASY FOR HIM OR HER TO TAXI ONTO RWY 13 THINKING HE/SHE IS INDEED ON RWY 17. SEVERAL INCIDENTS SIMILAR TO THIS ONE HAVE OCCURRED AT GGG. YET; NEVER DURING THEIR COMS; DID ATC MENTION THAT HOTEL IS AT THE INTXN OF 2 RWYS. A SIMPLE 'TAXI TO RWY 13; 17 INTXN VIA HOTEL;' WOULD ALERT THE PLT TO THE SITUATION. OR; WHEN CLRED TO BACKTAXI; A 'CROSS RWY 13 TO BACKTAXI 17' WOULD SUFFICE.