UNAUTH RWY OP. WRONG RWY ENTRY.

Narrative

EVENT OCCURRED DURING CLRNC FOR TKOF. AT CLE; RWY 23L AND 23R ARE IN CLOSE PROX. I WAS CLRED TO EXPECT TKOF ON RWY 23L (PER GND CTL); HOWEVER; ON STOPPING AT TXWY S; I WAS INFORMED THAT I HAD 5100 FT REMAINING FOR TKOF ON RWY 23R. I ACKNOWLEDGED AND SAID THAT THIS WAS ADEQUATE. ONGOING OVER TO TWR; I WAS CLRED FOR POS AND HOLD; RWY 23R WHILE I WAS STILL ON THE SE SIDE OF RWY 23L (TXWY L). BECAUSE OF POOR LIGHTING AND AN ANGLE OF THE XING TXWY; I MISSED THE TXWY INTXN WITH RWY 23L AND ENDED UP ON RWY 23L INSTEAD OF ACROSS IT AND ON RWY 23R. I NOTIFIED TWR (WORDS WERE 'MISSED THE TXWY'). TWR SENT LNDG TFC AROUND (1 AIRPLANE) AND THEN CLRED ME FOR IMMEDIATE TKOF ON RWY 23L (THERE WERE AT LEAST 3 MORE ACFT ON FINAL FOR RWY 23L) WHICH WAS ACCOMPLISHED WITH NO FURTHER DISRUPTION. CONTRIBUTING FACTORS WERE POOR LIGHTING; ILL-DEFINED TXWY/RWY DEFINITION AND THE ANGLE OF THE TXWY TO THE RWY NOT BEING 90 DEGS. I SHOULD NOT HAVE ACCEPTED THE CLRNC TO CROSS RWY 23L AND GO TO RWY 23R WHEN LNDG TFC WAS OBVIOUSLY CLOSE IN. HOWEVER; I WAS PREPARED TO TAKE THE GRASS TO THE R SIDE OF THE RWY 23L HAD THE TWR NOT INSTRUCTED THE NEAREST LNDG ACFT TO GAR. BETTER DEFINITION OF TXWY S BTWN RWY 23L AND RWY 23R WOULD HAVE MADE THIS INCIDENT MUCH LESS LIKELY TO HAPPEN.