LCL CTLR HAD JUST ASSUMED THE POS; WAS DISTR WITH OTHER DUTIES. CLRED ACFT X FOR TKOF. FORGOT ABOUT ACFT Y WHO WAS ON APCH. ACFT Y LANDED LONG OVER ACFT X.

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I HAD JUST RELIEVED THE PREVIOUS CTLR ABOUT 1 MIN EARLIER AND WAS TRYING TO ESTABLISH VERT SEPARATION BTWN A PREVIOUS ACR DEP AND A VFR CESSNA OVERFLT BEFORE SWITCHING THE ACR OVER TO DEP. I WAS ALSO TRYING TO TURN UP THE RADAR SCOPE'S MAP AND ALPHA NUMERIC BRIGHTNESS WHICH WAS VERY LOW WHEN ACFT X CALLED READY TO GO. I SCANNED THE RWY; BUT APPARENTLY NOT FAR ENOUGH ON FINAL. I CLRED ACFT X FOR TKOF AND RESUMED ADJUSTING THE SCOPE WHEN A SHORT TIME LATER ACFT Y; A LEAR ON FINAL AND CLRED TO LAND BY PREVIOUS CTLR; ASKED WHAT ACFT X WAS DOING. I LOOKED UP AND SAW THE LEAR ON SHORT FINAL WITH ACFT X PAST THE HOLD LINE WITH HIS NOSE OVER THE RWY EDGE. I TOLD THE LEAR TO GO AROUND. THE LEAR DID NOT RESPOND AND CONTINUED TO LAND. THE LEAR APPARENTLY THOUGHT THAT ACFT X WAS AT FAULT AND SAID HE CAUSED A RWY INCURSION. IT WAS MY FAULT. HAD I SET UP THE SCOPE PRIOR TO TAKING THE POS; OR SIMPLY TOLD ACFT X TO HOLD SHORT WHILE I WAS BUSY WITH THE DEPARTING TFC AND VFR TFC; AND TAKEN AN EXTRA MOMENT TO FULLY SETTLE IN TO THE POS; THIS INCIDENT WOULD NOT HAVE OCCURRED. ACFT X SAW THE LEAR ON SHORT FINAL AND STOPPED; BUT SINCE HE WAS PAST THE HOLD LINE; AN INCIDENT OCCURRED. I'VE HEARD THAT THE FIRST FEW MINS AND LAST FEW MINS ON POS ARE WHEN MOST INCIDENTS HAPPEN IN ATC; AND NOW I KNOW FROM EXPERIENCE. BE EXTRA VIGILANT WHEN TAKING THE POS AND DON'T LET THE FACT THAT THERE IS VERY LITTLE TFC LULL YOU INTO LETTING YOUR GUARD DOWN.