ACR LGT CLRED TO RWY 10R VIA TXWY A-S. RAINING AND POOR VISIBILITY AND TXWY MARKINGS. CROSSED RWY 10R IN ERROR AND LINED UP RWY 10L. NO CONFLICT AND TWR CLRED ACFT FOR DEP RWY 10L.

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IT WAS A DARK AND STORMY NIGHT. FROM ABEAM GATE OUR TAXI INSTRUCTIONS WERE TXWYS A AND S; RWY 10R. THE TXWYS WERE WET WITH RAIN COMING DOWN. THE PAINT LINES WERE NEARLY IMPOSSIBLE TO SEE. I WAS FO WITH MY HEAD DOWN AT TIMES WITH CHKLIST AND WT AND BAL UPDATES. IT WAS A SHORT TAXI TO A RWY WE DON'T FREQUENTLY USE. I SAW SOMETHING OFF TO THE R; AND TOLD THE CAPT I THOUGHT THAT MIGHT BE WHERE WE WERE SUPPOSED TO GO. CAPT THOUGHT THAT WAS AN INTXN AND CONTINUED TO FOLLOW ANOTHER ACFT TAXIING IN FRONT OF US. THERE WERE NO VISIBLE TXWY CTRLINE LIGHTS VISIBLE OR SIGNS WE SAW GOING TO RWY 10R. AS WE ARRIVED AT THE HOLD SHORT LINES FOR THE RWY; AT WHICH TIME TWR ADVISED US WE WERE ACTUALLY AT RWY 10L. OOPS! WITH APOLOGIES TO THE TWR; WE DEPARTED RWY 10L (US RWY 10R) WITH NO INCIDENT. WE HAD CROSSED JUST OFF THE END OF RWY 10R; BUT FORTUNATELY THAT RWY 10R WAS BEING USED ONLY FOR DEPS ONLY; AND NOT FOR ARRS. WHILE WE DID NOT CROSS THE ACTIVE RWY 10R; THE TXWY GOES JUST BEYOND THE APCH END OF RWY 10R; AND WE WOULD HAVE INTRUDED ON THE APCH PLANE HAD ANYONE BEEN ON APCH TO RWY 10R. SIGNAGE WAS HARD TO READ ON A WET; RAINY NIGHT; AND WE SAW NO TAXI LIGHTS TO RWY 10R; BUT WE ALSO MISINTERPRETED OUR LOCATION DURING THE SHORT; BUSY TAXI OUT.