B737 NG Captain reported EQUIP SMOKE light illuminated inflight.

Narrative

Aircraft was at cruise altitude FL330 when the EQUIP SMOKE light illuminated. Captain directed First Officer (FO) to continue as the Pilot Flying (PF) and Captain to complete the Non-normal checklist. Captain notified Dispatch of the situation and the possible need for a diversion. The EQUIP SMOKE light remained on and the checklist directed crew to make a landing at the nearest suitable airport. The Captain; First Officer and Dispatch all agreed on ZZZ as the best choice for diversion. Captain requested priority handling with ATC; gave them the SOB's; fuel remaining; no hazmat and requested new clearance for direct ZZZ. ATC cleared the flight via right turn direct ZZZ. Captain briefed Flight Attendants with Company Checklist and briefed passengers for unplanned landing. Flight proceeded uneventfully to ZZZ landing safely on Runway XXL. Airport Rescue and Firefighting (ARFF) had been requested by the flight crew. Crew was instructed to stop on runway to allow ARFF team to inspect aircraft. All clear was given and aircraft taxied safely to the gate followed by ARFF. Crew conducted informal debriefing. Captain and First Officer thanked everyone involved for their excellent performance.