A Tower Local Control trainee reported they cleared an aircraft for takeoff from the same runway a glider was being towed across.

Narrative

I was training on Local Control (LC) with 3 VFR planes in the pattern or sequenced to land. Aircraft X requests a Runway 30 departure with the Ground Controller (GC) and is taxied out on Runway 30. Aircraft X was instructed to hold short of Runway 06 due to landing Runway 6 traffic; but appeared to be holding short too close in the RSA. The landing traffic is issued a go around and after it passes Aircraft X is given a clearance to cross Runway 06. As Aircraft X crosses Runway 06 I give the GC the memory aid for the grass runway. I do not recall exactly what the GC said; but I took back the memory aid and continued to work the pattern traffic. I saw a glider being towed in the grass near Runway 30; but to me it appeared to be off to the side of the runway. Aircraft X calls on Tower when it is ready to depart and I wait for a departure gap with the landing 06 traffic. When I checked the Runway 30 I recall the towed glider still being off of the runway; however I still had the memory aid chip meaning GC and the glider have permission to cross that runway. I built a departure gap and clear Aircraft X for takeoff once Aircraft Y landing Runway 06 is through the intersection. I see the towed glider in the grass next to the runway; but it is now moving more towards the runway. My attention is drawn to Aircraft X taking a long time to start it's departure as the next arrival on 06 gets closer. It felt about 15 to 20 seconds of delay before Aircraft X was turned around and even rolling.The OS notices the glider is now on the Runway 30 and towing towards Taxiway A and points it out. My trainer and I both tell Aircraft X to cancel takeoff clearance and he comes to a stop short of Runway 24. The next arrival lands on Runway 06 without issue and Aircraft X later departs after back-taxiing for another departure on Runway 30. Factors on my side that led to this event include incorrect memory aid usage for the intersecting runway; continuously scanning while departing traffic instead of just once at the start; and assumptions that taxiing aircraft would hold short of Runway 30.The memory aid usage per our current SOP seems somewhat [counter]intuitive. You give away the memory aid when you have permission to use it; instead of having possession of the aid when you have permission. There are discussions of this being rewritten in the new SOP revision.Additionally if the permission to use the runway is not able to be given; part of the coordination should be to confirm both controllers understand the reason why.