What was found
NR 2 PEC CAUTION LIGHT AT CRUISE. DURING CLIMB WITH PROPS AT 900, NOTED FLUCTUATIONS OF +/- 10 RPM(890-910) FLUCTUATIONS INCREASED TO +/- 20 (880-920) AFTER LEVEL OFF FLUCTUATIONS CONTINUED AT PROPS 850 (830-870). AFTER 2 OR 3 MIN #2 PEC CAUTION LIGHT ILLUMINATED. PER E/A CHECKLIST MOVED CONDITION LEVERS TO 1020: PROP INDICATION ROSE TO 1040. CONTINUED TO FLUCTUATE +/- 20. PER CHECKLIST, (UNABLE TO CONTROL NP) CONTINUED TO ENGINE FAILURE INFLIGHT CHECKLIST. ENGINE SHUTDOWN. OPERATED SINGLE ENGINE REMAINDER OF FLIGHT. #2 ENGINE SHUTDOWN AND FEATHERED NORMALLY. GENERALLY #2 NP FLUCTUATED +/- 20 AT 900 AND 850 SETTINGS. AT 1020 SETTING IN DESCENT JUST PRIOR TO ENGINE SHUTDOWN REDIUCTION IN POWER LEVER(TRQ) WAS REQUIRED TO PREVENT NP OVERSPEED. AS POWER LEVER WAS OPERATED FURTHER, NP FLUCTUATED WITH POWER LEVER (WHILE #1 NP WAS STEADY AT 1020) AT ONE POINT, BACK TO APPROXIMATELY 930 RPM. DIVERTED AND ACCOMPLISHED UNEVENTFUL LANDING. REPLACED THE #2 ENGINE AND ALSO THE OIL COOLER AND THE #2 PROPELLER DUE TO OIL CONTAMINATION.