Southwest Airlines flight 2493 (SWA2493) and a Textron Aviation, Inc. 560XL (N564HV) were involved in a runway incursion with overflight that resulted in a loss of separation at San Diego International Airport (SAN). SAN was equipped with the Airport Surface Detection Equipment Model-X (ASDE-X) surface radar system. The system was operational and functioned as designed. It produced both aural and visual alerts that indicated that there was an aircraft [N564HV] landing with another aircraft [SWA2493] still in position on the same runway. The local control (LC) controller immediately reacted to the ASDE-X alerts, and issued instructions to resolve the conflict, but not before standard separation had been lost. The SAN Airport Traffic Control Tower (SAN ATCT) facility was equipped with two flight strip printers, one functioned as a primary device, and the second as a backup in case the first unit failed. In post incident interviews, the SAN ATCT personnel stated that they received no training on the use or troubleshooting of these printers. Prior to the incident, the primary printer jammed. During the post-incident interview with the operations supervisor (OS), they stated that they chose to troubleshoot the primary printer rather than switching to the backup, and that this drew their attention away from the operation at the time of the incident. FAA Order JO 7110.65BB, Air Traffic Control, 2-10-3, Tower Team Position Responsibilities, states in part: Tower Team Concept and Intent: There are no absolute divisions of responsibilities regarding position operations. The tasks to be completed remain the same whether one, two, or three people are working positions within a facility/sector. The team, as a whole, has responsibility for the safe and efficient operation of that facility/sector. The LC controller noticed a flight strip at their workstation that indicated an initial altitude for an uninvolved departing aircraft that was not in accordance with facility directives and contacted Southern California Terminal Radar Approach Control (SCT TRACON) to coordinate an appropriate altitude. This diverted their attention from N564HV and SWA2493 momentarily. During the post-incident interview conducted with the LC controller, they stated that they had used poor judgment in prioritizing their duties. This duty prioritization was not consistent with guidance contained in FAA Order JO 7110.65BB, Air Traffic Control, 2-1-1, ATC Service.