A B737-300 WAS DISPATCHED WITH A DEFERRED CTR HYDRAULIC PUMP. ON CLBOUT; FLT CREW OBSERVED A CTR SYS HYDRAULIC PRESS EICAS MESSAGE. NO MEL WARNING THAT EICAS MESSAGE WILL OCCUR WITH THE DEFERRAL.

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ON CLBOUT; WITH C2 ELECTRIC HYDRAULIC PLACARDED INOP AND SWITCH OFF PER COMPANY POLICY; WE GOT AN UPPER EICAS CTR SYS HYDRAULIC PRESSURE AMBER MESSAGE. WE CHKED LOWER EICAS AND FOUND CTR SYS PRESSURE AT 3000 PSI. THE ISLN LIGHT ON THE RESERVE BRAKES TEST PANEL ON THE P6 PANEL WAS ON AS WELL. THIS APPEARS TO BE BOEING LOGIC INDICATING THAT THERE WAS A SWITCH OFF THAT WOULD NORMALLY BE ON; NAMELY THE C2 ELECTRIC PUMP SWITCH. ALL MEL CAVEATS HAD BEEN COMPLIED WITH BY MAINT AS WELL AS OURSELVES. I HAD HAD THE FEELING THAT 'SOMETHING WASN'T QUITE RIGHT' BUT COULDN'T PUT MY FINGER ON IT IN THE GATE SO I TRUSTED OUR MAINT PEOPLE TO GET IT RIGHT. MY CREW AND I AGREED THAT WE WANTED TO SEE WHAT WOULD OCCUR IF WE TURNED ON THE C2 ELECTRIC PUMP AGAIN AS IT HAD BEEN CONFIRMED IN THE GATE THAT IT WOULD POWER UP. I DECIDED TO USE MY EMER AUTHORITY TO TRY THE C2 PUMP SWITCH ON RATHER THAN RUN A QRH CHKLIST THAT DIDN'T SEEM TO APPLY. WHEN WE DID; THE EICAS AMBER WARNING WENT OUT AND ALL APPLICABLE LIGHTS RETURNED TO NORMAL INCLUDING THE C2 ELECTRIC HYDRAULIC PUMP 'PRESS' LIGHT IN THE SWITCH. WE CONTINUED UNEVENTFULLY TO ZZZZ WITH NO FURTHER INDICATIONS OR PROBS; ALTHOUGH; TO OUR RECOLLECTION; THE ISLN LIGHT REMAINED ON ON THE RESERVE BRAKES TEST PANEL ON P6. WE WERE INFORMED IN ZZZZ THAT THE OUTBOUND CREW HAD SIMILAR WARNINGS OCCUR ON THEIR CLBOUT WITH ADDED MESSAGES AND THAT THEY HAD RUN THE CTR SYS LOSS OF PRESSURE CHKLIST AND RETURNED TO ZZZZ LNDG OVERWT. I RECOMMENDED IN ESSENCE THAT THE MEL NOTES FOR THE C2 PUMP BE AMENDED TO INCLUDE THAT THE EICAS WARNING WILL OCCUR AFTER TKOF WITH THE PUMP SWITCH IN THE OFF POSITION; AND FOR THE CREW TO THEN CANCEL THIS EICAS MESSAGE INSTEAD OF BEING TEMPTED TO TURN THE PUMP BACK ON AT THAT TIME. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THIS AIRPLANE WAS TAXIED TO THE TERMINAL BY MAINT TECHNICIANS WHO WERE REQUIRED TO MAKE SOME TESTS THAT AT ONE TIME THE FLT CREW ACCOMPLISHED. THIS RPTEDLY WAS A COMPANY PROC CHANGE THAT ALLOWED THE FLT CREW TO SHORTEN THE PREFLT CHK. RPTEDLY THE MAINT CREW DEFERRED THE CTR HYDRAULIC SYSTEM PUMP SYSTEM FOR WHATEVER REASON AND PLACARDED THE SYSTEM PER THE MEL. ON CLBOUT; THEY GOT AN EICAS WARNING THAT WAS NOT EXPECTED 'EICAS CTR SYS HYDRAULIC PRESSURE.' THE RPTR STATED THE PLACARDING FOR THIS DEFERRED ITEM IS WRONG AND SHOULD STATE THE EICAS WARNING WILL APPEAR AFTER TKOF AND JUST CANCEL THE EICAS MESSAGE. THE RPTR BELIEVES BETTER TRAINING FOR THE TAXI CREWS MAKING THE SYSTEM CHKS WOULD AVOID FLT PROBS. THE RPTR STATED THEY REVIEWED THIS RPT WITH FLT OPS TRAINING DEPT.