Date: 202010
Local time of day: 1201-1800
Location: ZZZ.Airport, US
Weather elements / visibility: 10
Aircraft: Small Transport; Low Wing; 2 Turbojet Eng
Operator: Personal
Operating under: Part 91
Flight plan: IFR
Mission: Training
Flight phase: Taxi
ATC / advisory: Tower ZZZ
Second aircraft: Commercial Fixed Wing
Reporter organization: Personal
Reporter function: Pilot Flying; Single Pilot
Human factors: Distraction; Situational Awareness; Confusion
Second reporter function: Ground
Anomaly: Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance; Ground Incursion Taxiway
Detector: Person Flight Crew
When detected: Taxi
Result: Air Traffic Control Provided Assistance; Flight Crew Requested ATC Assistance / Clarification
Contributing factors: Staffing; Procedure; Human Factors; Environment - Non Weather Related; Airport
Primary problem: Human Factors

Narrative: Upon landing on Runway XXR at ZZZ; I exited on Taxiway 1 and turned left at Taxiway 2.  The Controller asked my parking spot.  I replied 'Company X.'  Controller gave me taxi instructions and I replied 'Taxiway 3; Taxiway 4; cross Runway Y; into parking.'  At intersection of Taxiway 2 and Taxiway 3; I turned left instead of right and taxied across Runway XXL.  There was Aircraft Y on departure from Runway XXR already past me.  Once I realized my mistake of turning left on Taxiway 3 instead of right; I stopped and told the Ground Controller.


Second narrative: Most of the 1 hr and 40 minutes I had been on position with positions combined during moderate to busy traffic. I had been held over for 2 hours and a Supervisor was working LC with Tower in-charge on a single runway; so we were not using LUAW (Line Up And Wait). Additionally Runway XXL was closed as well (which we use to offset small arrivals to allow for more departures on XXR) and all these factors were adding complexity to an already busy session.Aircraft X exited Runway XXR and was given taxi instructions 'Taxiway 2; Taxiway 3; Taxiway 4; cross Runway Y and taxi to park' (Runway Y is a closed runway in my control). The pilot read back the instructions correctly. I had other aircraft taxiing and needed a runway crossing between the steady stream of arrivals and departures. I coordinated for the crossing with LC and after Aircraft Y went through the intersection on takeoff roll; I cleared the aircraft waiting to cross Runway XXR at Taxiway 5 to cross. I watched him cross; checked another plane taxiing to the runway; checked the printer for clearances; checked back on my crossing; and informed LC the Taxiway 5/XXR crossing was complete. At that point Aircraft X keyed up and said something like 'Uh; GC? I think we took a wrong turn.' I did a quick scan of the runway and didn't see him initially because one of the poles was in the way. I started to key up to ask him where he was and stepped back to re-scan and realized he was on the north side of XXR half on the runway and half off. I immediately informed LC of the situation. I turned Aircraft X around and held him short of XXR and told local I was too busy to find a hole to cross him and to just call me when he had a place for me to cross him back over. I informed the pilot of his possible pilot deviation and gave him the phone number and then moved on to other planes and clearances. This is an intersection we have had multiple issues with for runway incursions and last I knew is identified as a hot spot on the chart. Recently the airport added wig-wags to make it clear that it is a runway intersection to help stop pilots from doing this. ZZZ needs some sort of ground radar because even with the new safety lights installed they still cross. Some sort of early warning from an ASDE would at least give us a chance to catch this sort of thing.While the Supervisor was doing a very good job of working LC; I was still trying to keep my eye on him because of how little pro-time they need; the regular decrease in traffic from COVID slowing our skills; and the high volume of traffic he was working as well. If the traffic is regularly that volume at that time of day; it's imperative that three people be in the Tower; not two. The only way I could have caught this aircraft would have been if I was staring directly at him as he made the turn. The distance from Taxiway 2 to Runway XXR on Taxiway 3; is very short and I was focused on verifying the completion of the runway crossing Taxiway 5.Recommend 3 people in the tower from XA-XC pm.


Synopsis: Pilot and Controller reported a runway incursion due to the pilot misunderstanding of ATC's clearance.