B787 First Officer reported during engine start they received a fire warning in one engine and were towed back into the gate.

Narrative

During engine start the EICAS 'OVERHEAT ENG R' WITH CHECKLIST ICON appeared. The right EGT was slightly higher by only 20 degrees or so. The Overheat EICAS was coming on and off. First Officer (FO) began to run the checklist then the FIRE INDICATIONS on the right engine started (bell+lights). Engine was secured and fire handle pulled but light went out so no bottles were discharged. Crew called ramp on XXX.XXX to have the fire department come and inspect the right engine. I don't recall if the FO actually advised ATC at that time as I was helping the Captain deal with the checklists/actions. Over 10-15 minutes passed before any emergency vehicles showed up. Responders found nothing of concern so we hooked up to a tug and towed back into gate XX at XA:00. Gate agents were prompt arriving at the jetway and opening the cabin door. Passengers remained onboard while maintenance inspected the aircraft. Ultimately the flight cancelled but the cancellation determination took nearly 2 hours. Crew reviewed required reporting Items: Dispatch notified; chief pilot briefed; reports made.