ACFT TAXIING ON PRC ENTERED RWY WITHOUT ATC CLRNC.

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I WAS PROVIDING OJT INSTRUCTION TO A CTLR IN TRAINING. THE PIC OF THE HARMON ROCKET REQUESTED TAXI INSTRUCTIONS FROM THE NW SIDE OF THE ARPT TO THE SE SIDE OF THE ARPT. THIS WOULD REQUIRE XING THE ACTIVE RWY. THE PLT OF THE ROCKET WAS INSTRUCTED BY THE TRAINEE TO HOLD SHORT OF RWY 21L AT TXWY C3. THE PLT OF THE ROCKET READ BACK THE HOLD SHORT INSTRUCTIONS. I OBSERVED THE ROCKET APCHING THE HOLD BARS ON TXWY C3 AND DETERMINED THAT THE ACFT WAS NOT GOING TO STOP. I INSTRUCTED THE PLT OF THE ROCKET TO 'STOP.' THE ACFT STOPPED BTWN THE HOLD BARS AND THE RWY EDGE. THE PLT STATED 'I AM HOLDING SHORT OF THE RWY.' I ADVISED HIM THAT HE WAS ABOUT 40 FT PAST THE HOLD BARS. I ALSO ADVISED THE LCL CTLR THAT HIS RWY WAS NOT CLR. THE DEPARTING DUCHESS WAS ROTATING AND WAS AT APPROX 200 FT AGL AS HE PASSED TXWY C3. SUPPLEMENTAL INFO FROM ACN 574326: CALLED GND FOR CLRNC TO TAXI FROM MY HANGAR TO A MAINT FACILITY ON THE OTHER SIDE OF THE FIELD; ACROSS THE ACTIVE RWY 21L. INITIALLY I WAS TOLD: 'TAXI VIA TXWY A; THEN THE N RAMP; HOLD SHORT OF RWY 21L ON TXWY C4.' THERE WAS ALREADY ANOTHER ACFT HOLDING AT TXWY C4 SO THEY SAID 'NOW TAXI VIA TXWY B TO TXWY C; HOLD SHORT OF RWY 21L AT TXWY C3.' NORMALLY I WOULD HAVE BEEN CLRED TO CROSS THE ACTIVE AT TXWY 4; A DIRECT RTE. WHEN I ARRIVED AT TXWY C3; WHICH IS A DIAGONAL TXWY; I COULD SEE THAT I WOULD PROBABLY BE CLRED TO CROSS THE ACTIVE ON TXWY E; WHICH JOINS TXWY C3 AT AN ANGLE. I WAS FOCUSED ON THE TXWY/RWY SIGNS THERE TO MAKE SURE THAT I WOULD BE LIED UP FOR TXWY E; WHEN I REALIZED I HAD CROSSED THE HOLD SHORT LINE. I STOPPED IMMEDIATELY. GND SAID 'STOP!' I SAID 'I AM ALREADY STOPPED.' THEY REPLIED 'YES; BUT YOU ARE ALREADY WELL PAST THE HOLD SHORT LINE.' THIS WAS TRUE. I ESTIMATE THAT I WAS ABOUT 1 FUSELAGE LENGTH BEYOND THE LINE. I WAS THEN CLRED ACROSS THE ACTIVE TO Y DET. NO ACFT WERE TOLD TO GO AROUND OR HOLD TKOF. SO WHAT CAUSED THE PROB? TOO NARROW A FOCUS ON MY PART. AN UNUSUALLY CIRCUITOUS TAXI RTE TO AN UNFAMILIAR XING POINT CAUSED ME TO CONCENTRATE ON THE TAXI RTE AND MISS SEEING THE HOLD SHORT LINE UNTIL I WAS XING IT. A CONTRIBUTING FACTOR WAS THAT MY ACFT IS A TAIL-DRAGGER; WHICH HAS VERY LIMITED FORWARD VISIBILITY ON THE GND; REQUIRING S-TURNS TO SEE AHEAD. I STILL SHOULD HAVE ANTICIPATED THE HOLD SHORT LINE AND SEEN IT IN PLENTY OF TIME TO STOP. I NEEDED TO MAINTAIN A WIDER SCAN. LESSON LEARNED.