CPR X TKOF ON OCCUPIED RWY HAD LTSS FROM VEHICLE ON RWY. SYS ERROR.

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I WAS ASSIGNED TO WORK LCL CTL/GND CTL COMBINED POS; WHICH IS NOT UNCOMMON AT OUR CTL TWR WHEN TFC VOLUME IS LIGHT. AN ARPT VEHICLE WAS OUT ON RWY 36 WITH A CREW PULLING WEEDS. THE RWY WAS NOT OFFICIALLY CLOSED. RWY 31 WAS THE ADVERTISED ACTIVE RWY. THERE WERE PATCHES OF GND FOG OBSCURING PORTIONS OF THE ARPT SURFACE ALTHOUGH WE WERE VFR. AT SOME POINT; A FOG BANK CAME OVER THE NORTHERN END OF RWY 36 AND COVERED THE VEHICLE AND GND CREW. CPR X CALLED FOR TAXI AND I TOOK HIM TO RWY 36 THINKING THAT IT WOULD EXPEDITE TFC AND KEEP HIM AWAY FROM OPS ON RWY 31. WHEN CPR X CALLED READY ON TWR FREQ; I CLRED HIM FOR TKOF ON RWY 36. I FIRST BECAME AWARE OF THE OPERROR WHEN THE PLT ASKED ME IF I WAS AWARE THAT A TRUCK WAS ON THE RWY. HERE ARE WHAT I BELIEVE WERE THE CONTRIBUTING FACTORS: I FAILED TO INCLUDE A THOROUGH SCAN OF MY NOTEPAD WITH MY SCAN OF THE RWY. THE MEN WORKING ON THE RWY ONLY HAD A RADIO IN THE TRUCK. THEY COULD NOT RESPOND TO HEARING ME TAXI THE ACFT; NOR TO MY CLRING HIM FOR TKOF. I HAD GOTTEN USED TO SEEING THE VEHICLE OUT THE WINDOW AND DID NOT TAKE SPECIAL NOTE THAT IT MIGHT DISAPPEAR IN THE FOG. UNUSUAL OPS AND REQUESTS FROM PLTS OPERATING ON RWY 31 DIVERTED MY ATTN FROM OTHER OPS ON THE FIELD. SUNLIGHT; FALLING ON OUR BLINKING ARPT OPS LIGHT; WASHED OUT THE LIGHT AND DIDN'T CATCH MY EYE. SUPPLEMENTAL INFO FROM ACN 222950: I WAS PIC OF CPR X. WE RECEIVED CLRNC TO TAXI TO RWY 36. AFTER COMPLETING OUR PRE-TKOF CHKLISTS; WE WERE CLRED BY THE TWR TO 'TAXI INTO POS AND HOLD.' WE HELD IN POS FOR ABOUT 1 1/2 MINS DUE TO TFC ON RWY 31. THE TWR CLRED US FOR TKOF AND I BEGAN A NORMAL TKOF. AFTER ROTATING THE ACFT AND RAISING THE GEAR; BOTH THE COPLT AND I SAW A TRUCK ON THE RWY. I ESTIMATE WE PASSED OVER TOP OF THE TRUCK BY 50 TO 100 FT. THE WX WAS CLR AND; ALTHOUGH THERE WAS SOME PATCHY GND FOG; IT WAS NOT A FACTOR IN THIS INCIDENT. THE SLOPE OF THE RWY AND THE TRUCK'S LOCATION MADE IT DIFFICULT; IF NOT IMPOSSIBLE; TO SEE THE VEHICLE UNTIL ROTATION. THE TRUCK'S LOCATION PRECLUDED A PROB AS A NORMAL TKOF WOULD PASS WELL ABOVE THIS POINT. WE RECEIVED NO INDICATION OF ANY OBSTRUCTION ON OR NEAR THE RWY. OUR TAXI AND TKOF CLRNCS WERE NORMAL.