A TUG TOWING A B737 TO A TERMINAL GATE WITH NO GND CTL OR COCKPIT COMS CROSSED AN ACTIVE RWY WITHOUT CLRNC.

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ON AUG/XY/98 AT APPROX XA30 I WAS ASSIGNED TO DELIVER ACFT XYZ FROM ZZZ SPOT X TO GATE BC. AFTER RECEIVING THESE INSTRUCTIONS I WENT DIRECTLY TO THE ACFT PICKING UP THE LOGBOOK AND A TOW BAR (TB Y) ALONG THE WAY. AFTER CONNECTING THE TOW BAR TO THE ACFT; I STARTED A THOROUGH WALKAROUND INSPECTION; NOTING 2 NEW NLG TIRE INSTALLATIONS. I WENT UP INTO THE CTL CABIN TO DOUBLECHK SYS CONFIGNS AND CONFER WITH XXY THAT WE WERE READY TO GO; 'B' PUMP; ANTISKID; BEACON; NAV LIGHTS; ETC. AFTER STARTING THE TRACTOR; I PLUGGED THE INTERPHONE CORD TO MY HEADSET AND TRIED TO CALL XXY. THERE WAS NO SIDE TONE OR RESPONSE; SO I WENT TO THE BACK OF THE TRACTOR TO THE SECOND INTERPHONE CONNECTION POINT; PLUGGING MY HEADSET IN THERE; ATTEMPTING TO TROUBLESHOOT AND HOPEFULLY ELIMINATE MY COM PROB; NO JOY. THEN I PLUGGED DIRECTLY INTO THE ACFT'S INTERPHONE JACK AND COULD HEAR SIDE TONE. I CALLED XXY; TOLD HIM WE WERE OUT OF TIME; I HAVE 2 BAD CORDS; HE WOULD HAVE TO RELAY THE GATE CLRNC INFO TO ME OUT HIS WINDOW (L-HAND) WHEN WE STOPPED AT THE ZZZ W GATE. AFTER RELEASING THE BRAKES (APPROX XC00) STARTING MY TOW; I TURNED ON THE TRACTOR'S RADIO EXPECTING TO HEAR THE TWR GIVING OTHER ACFT INSTRUCTIONS; BUT I COULDN'T HEAR ANY XMISSIONS AT ALL. WHILE TOWING I TRIED TURNING THE RADIO ON AND OFF; AND RECHANNELIZING; BUT STILL I COULD HEAR NOTHING. XXY SAID 'CLRED ON S; HOLD RWY 28R.' I REPEATED THE INSTRUCTIONS RECEIVING A THUMBS UP; I SAID 'OK; YOU'LL NEED TO HANDLE ALL OF OUR COMS; ANY PROBS AT ALL JUST HIT ME WITH A LNDG LIGHT AND I'LL STOP.' HE SAID OK! STOPPING ON TXWY S AT RWY 28R; I SAT IN THE TRACTOR SCANNING ALL THE ACTIVITY ON THE FIELD; NOTING 2 ACFT DOWN THE RWY; THEY APPEARED TO BE ON THE RWY 28L. 1 OF THE ACFT ON THE RWY HAD ALL OF ITS LIGHTS ON; CHARACTERISTIC OF AN ACFT THAT HAD JUST LANDED. IT SEEMS TO ME (RECOLLECTION NOT CLR ON THIS POINT); I OBSERVED AN ACFT LAND ON RWY 28R AND TAXI OFF WHILE WE WAITED HOLDING RWY 28R. I SAT IN THE TRACTOR ABOUT 3 OR 4 MINS BEFORE DISMOUNTING AND STEPPING OUT INTO VIEW OF THE COCKPIT. WHEN I DID THIS XXY STUCK HIS L ARM OUT OF THE COCKPIT WINDOW AND POINTED ACROSS THE (OUR END) END OF THE RWY. I THOUGHT HE WAS INDICATING WE HAD CLRNC TO CROSS THE RWY 28R! I MOUNTED THE TRACTOR AND RESUMED MY TOW IMMEDIATELY. STILL TRYING TO GET THE RADIO TO WORK; I TURNED THE SQUELCH CTL KNOB AND THE RADIO CAME ALIVE BLARING. AFTER GETTING THE VOLUME UNDER CTL I COULD HEAR TWR CALLING ACFT XYZ AS I WAS APCHING RWY 28L...S...B...UNREADABLE. I ASKED FOR REPEAT INSTRUCTIONS. AGAIN...CONTINUE ON S...B...UNREADABLE! I CALLED ONCE MORE TELLING THE TWR THAT I WAS HAVING RADIO DIFFICULTIES; 'UNDERSTAND CONTINUE ON S; B...TO THE GATE.