Ground Controller described a potential ground conflict when taxiing traffic failed to stop short of the hold lines; the reporter indicating miscommunication within the tower cab.

Narrative

I was working Ground Control [for] Runway XX; Runway YY in use. A Sovereign called ready to taxi. I gave the Sovereign taxi instructions to Runway YY to cross Runway XX at Taxiway A. The Sovereign was witnessed coming south on Taxiway A; and more aircraft were taxied in and out to the active runway. Another aircraft was awaiting a release in the Taxiway L side run-up area. This aircraft reported a coyote near the approach end of the runway. This caused some distraction to the operation and while rearranging my flight strips; I looked up and a Twin Cessna was landing Runway XX. I immediately looked for any possible conflicts and noticed the Sovereign was stopped on Taxiway A short of Runway XX but beyond the hold short lines. The hold short line appeared to be between the nose and main gear. With no other conflicts; I apologized to the Sovereign and told [him] to cross Runway XX continue to Runway YY. I then completed any remaining runway crossings and released Runway XX to Local Control. I recommend supervisors and staff personnel be required more currency time.