BOTH OVERHEAD REVERSER LIGHTS ILLUMINATED WHILE A B737-400 WAS IN LEVEL CRUISE FLT. THE OVERHEAD MASTER CAUTION LIGHT DID NOT ANNUNCIATE. AN EMER WAS DECLARED WITH A DIVERSION.

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APPROXIMATELY ABEAM ZZZ CAPT NOTICED THE TWO REVERSER LIGHTS ON OVERHEAD. WE WENT TO THE QRH AND NOTIFIED DISPATCH AND MAINT VIA ACARS. WE WERE NOTIFIED BY MAINT TO DIVERT TO ZZZ1 FOR MAINTENANCE. WE DECLARED AN EMERGENCY AND DIVERTED TO ZZZ1 WHERE MAINTENANCE HAD PARTS SENT FROM ZZZ2 TO ZZZ1. WE DEPARTED APPROXIMATELY TWO HOURS LATER WITH ALL PASSENGERS. NO OTHER EVENTS OCCURRED.CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE REPORTER STATED THAT THIS ACR DOES NOT REQUIRE FLT CREWS TO CARRY ACFT SYSTEMS MANUALS WHILE AT WORK AND NO MANUALS ARE KEPT WITH THE ACFT. IN THIS CASE; THE REPORTER HAD A MANUAL IN THEIR FLT BAG BECAUSE AS A CHECK AIRMAN FREQUENT SYSTEMS QUESTIONS ARE RAISED BY PILOTS NEW TO THE ACFT AND THERE ARE NO OTHER REFERENCE MATERIALS AVAILABLE. THE CREW ONLY REALIZED THE SERIOUSNESS OF THE REVERSER ANNUNCIATIONS AFTER LOOKING AT THE MANUAL AND THEN WERE VERY CONCERNED ABOUT A REVERSER(S) DEPLOYING IN FLT. WHEN THE ACFT TOUCHED DOWN AT LANDING THE LIGHTS EXTINGUISHED WHICH THEY SHOULD HAVE BECAUSE THE REVERSER ISOLATION VALVES ALLOWING THE REVERSERS TO DEPLOY ARE NOW AVAILABLE FOR BRAKING ASSISTANCE. THE ACFT WAS ON THE GND APPROXIMATELY 3 HOURS AND THE BOX CONTROLLING THE REVERSERS WAS CHANGED. THE FLT CONTINUED TO ITS ORIGINAL DESTINATION WITH NO FURTHER ANOMALIES.