UNAUTH RWY OP TAXI OP WHEN COMMUTER PIC MAKES A WRONG TURN ON A TXWY AND GETS ONTO A RWY HE WAS CLRED ONLY TO CROSS. VISIBILITY REDUCED; WX FACTORS. TERMINAL AREA WX.

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CALLED FOR TAXI. GND CTLR TOLD US TO TURN AT TXWY A TO RWY 22R. I WAS TAXIING SLOWLY AND LOOKING FOR SIGNS. AT A GLANCE I PICKED TXWY A SIGNS WHICH WERE IN THE MIDDLE OF A WHOLE BUNCH OF OTHER YELLOW AND BLACK TXWY SIGNS. I SHOULD HAVE MADE A 90 DEG TURN ONTO TXWY A BUT THERE WAS ALSO TXWY K WHICH WAS RIGHT AT ENTRY POINT OF TXWY A EXCEPT IT WAS MORE LIKE A 120 DEG TURN. I TURNED ONTO TXWY K BY MISTAKE SIMPLY BECAUSE IT CAME UP FIRST. ALSO IT WAS HARD TO KNOW THE DIFFERENCE BTWN A TURN THAT'S 90 DEGS OR 120 DEGS IN THE FOG. AS SOON AS I REALIZED WE DEVIATED FROM CLRNC; I HAD THE FO CALL THE GND CTLR AND TELL THEM WHERE WE ARE; AND WE ARE CORRECTING. TOTAL LOST TIME WAS ABOUT 20 SECONDS; ENOUGH TO END UP IN THE MIDDLE OF RWY 1/19. RWY 1/19 WAS NOT ACTIVE AND WE HAD CLRNC TO CROSS IT. WE ENDED UP TAXIING ON RWY 1/19 FOR ABOUT 50 FT AND MADE GND CTLR AWARE OF THAT. THERE WAS NO TFC CONFLICT BTWN US AND OTHER TAXIING; TAKING OFF; OR LNDG TFC. THE FO WAS BUSY FIGURING OUT THE PWR AND AIRSPD DATA. THE COMPANY MAKES US DO THAT WHILE TAXIING. HAD THE FO BEEN LOOKING OUTSIDE; SHE MIGHT HAVE CAUGHT THE MISTAKE. AT THE TURNING POINT I WAS LOOKING IN AND OUT TO ADJUST ALTIMETER; AIRSPD BUG AND PWR; ETC. SUPPLEMENTAL INFO FROM ACN 356909: I; AS THE FO; SHOULD HAVE PAID MORE ATTN DURING TAXI WITH LOW VISIBILITY; ESPECIALLY CLOSE TO THE RWY.