A Tower Controller assigned CIC duties combined with Local Control reported they were distracted discussing an equipment problem with maintenance personnel when a light aircraft landed on the same runway as an air carrier was cleared for takeoff from.

Narrative

I was working local control and was TCIC (Tower Controller in Charge). Aircraft X was cleared to land RWYXX. Aircraft Y was approaching RWYXY ready for takeoff with a imminent TMU flow control time. At the same time 3 tech ops personnel approached me to discuss the ILS control panel that had been in constant alarm all day; and the night before. I then cleared Aircraft Y for takeoff on RWYXY. The data tag for Aircraft X had dropped and the aircraft was difficult to see because of cloudy skies and it is small. I scanned the runways and saw Aircraft X exiting RWYXX at taxiway 1. Since Aircraft X had already turned off of the runway before Aircraft Y started its departure roll there was no need to cancel its takeoff clearance. Staff ZZZ ATCT appropriately. Lack of appropriate staffing and a ground controller only certified on GC; required the local controller to also be TCIC. Had there been a stand alone TCIC or if GC was able to be TCIC; the local controller would not have been distracted by tech ops personnel and maintenance issues.