A B767-200 flight crew encountered a REV (engine reverser not stowed) warning. Visual inspection seemed to indicate partial deployment so they declared an emergency and diverted to the nearest suitable airport.

Narrative

At approximately XA20Z; FL390 Mach .814; the 'Reverser' annunciation came on amber over the right N1 display. I was the Pilot Flying; so I maintained aircraft control; while the Captain ran the Quick Reference Handbook 767 'Reverser Unlocked' checklist contained in PB 757/767. Since there was no yaw; loss of airspeed or buffet; the checklist ended with 'operate the engine normally.' The Captain elected to contact Maintenance Control via a patch through Dispatch. Maintenance Control advised to look at the engine. The Captain sent me back to do this. I reported that the reverser sleeve appeared to be slightly deployed. Based on this information and advice from Maintenance Control; we decided to land at ZZZ. ATC began giving us vectors to ZZZ. Since the sleeve was in fact deployed; we decided to do the rest of the Quick Reference Handbook checklist which involved shutting down the engine (single engine time was 12 minutes). The checklist also called for a no-slats/flaps 20 degree landing; and that is how we landed. The landing was; of course; fast but otherwise uneventful and not overweight. We taxied normally to the gate. Note: as we slowed after landing; the Reverser annunciation went out and on walkaround we found the sleeve fully stowed. After the aircraft was serviced by Maintenance and the Quick Turn Around chart was complied with; we departed for ZZZ1.