LEAR35 FLT CREW DEPARTING MYEF HAS PRESSURIZATION PROBLEMS AND APPROACHING 10000 FEET REQUESTS TO 'STAY LOW' FOR TROUBLESHOOTING. DURING TROUBLESHOOTING THE ACFT DESCENDS TO 6300 FEET.

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WHILE CLBING OUT AFTER TKOF; THE CABIN DID NOT INITIALLY PRESSURIZE. IT WAS QUICKLY (WITHIN 1000 FT OF FIELD ELEVATION) DISCOVERED THAT THE CABIN AIR WAS NOT TURNED ON. THE CAPT QUICKLY TURNED THE SWITCH TO TURN THE CABIN AIR ON; HOWEVER; THE CABIN STILL FAILED TO PRESSURIZE AND THE 'CABIN AIR' LIGHT CAME ON. THE CTLR CLRED US TO CLB TO 27000 FT. I ASKED THE CTLR IF WE COULD STAY AT A LOWER ALT AND THAT WAS APPROVED. WE WERE APPROX 10000 FT AT THIS TIME. THE CAPT WAS TRYING TO REMEDY THE SITUATION AND THE EMER PRESSURIZATION SYS KICKED ON. THE CABIN THEN SLOWLY STARTED TO DSND AND THE CAPT REALIZED THAT THE PRESSURIZATION WAS SET TO 'MANUAL' INSTEAD OF 'AUTO;' THUS PREVENTING THE CABIN FROM CLBING. IN THE INTERIM; THE CAPT ELECTED TO DSND FURTHER TO STABILIZE THE CABIN AND ELIMINATE THE CABIN ALARM; EVENTUALLY LEVELING AT APPROX 6500 FT. THE CABIN THEN NORMALLY PRESSURIZED WITH NO FURTHER ISSUES. THE CTLR LATER ASKED IF EVERYTHING WAS OK; TO WHICH THE CAPT RESPONDED IN THE AFFIRMATIVE. IF THE CTLR ASKED US TO LEVEL AT 10000 FT AND NOT DSND FURTHER; THAT WAS NOT UNDERSTOOD BY THE CREW. FINALLY; THE CTLR STATED THAT WE WERE NOW IN A DIFFERENT AGENCY'S AIRSPACE WITHOUT PERMISSION AND GAVE US A TELEPHONE NUMBER TO CALL UPON LNDG. AFTER LNDG AND AFTER CLRING CUSTOMS (THE CALL TO THE CTLR WAS MADE BY THE CAPT AFTER CLRING BECAUSE CUSTOMS PROHIBITS CREWS FROM USING CELL PHONES ANYWHERE NEAR THEIR BUILDING IN A SECURITY EFFORT); THE CAPT; WHO MADE THE TELEPHONE CALL WITHOUT MY PRESENCE; TOLD ME THAT EVERYTHING WAS 'OK' AND THE SITUATION WAS HANDLED. I BELIEVE THAT WHILE RUNNING THE AFTER-LNDG CHKLIST AT THE DEP ARPT (MY FLYING LEG); THE CAPT NOT ONLY TURNED OFF THE 'CABIN AIR' AS CALLED FOR BY THE CHKLIST; BUT HE ALSO TURNED THE CABIN AIR SWITCH FROM AUTO TO MANUAL. THIS WAS NOT CAUGHT ON THE TAXI OUT FROM THE ARPT (CAPT'S LEG). I; AS THE PNF ON THE DEP LEG MADE A MISTAKE IN NOT TURNING ON THE CABIN AIR ON TKOF; HOWEVER; I DO NOT THINK THIS CAUSED OUR CABIN ALT WARNING BECAUSE IT WAS QUICKLY TURNED ON RIGHT AFTER TKOF AND WOULD NOT HAVE LED TO OUR SITUATION. I BELIEVE THE 'REAL' CAUSE OF OUR PRESSURIZATION ISSUE WAS CAUSED BY THE CAPT'S SWITCHING THE SYS FROM 'AUTO' TO 'MANUAL' UPON LNDG. I THINK THAT THE SITUATION COULD HAVE BEEN HANDLED BETTER AND ANY POSSIBLE INADVERTENT AIRSPACE VIOLATION COULD HAVE BEEN AVOIDED HAD THE CAPT CALLED FOR THE APPROPRIATE (CABIN LIGHT) CHKLIST SOONER AND HAD BETTER COMS BEEN MADE BTWN US AND THE CTLR; IE; CLRLY STATING THAT WE WOULD NEED TO CONTINUE TO DSND TO A CERTAIN ALT DUE TO THE NATURE OF THE SITUATION (PRESSURIZATION) WE WERE ATTEMPTING TO FIX INSTEAD OF JUST VAGUELY STATING THAT WE WANTED TO DSND TO A 'LOWER ALT.' ALSO; I THINK THAT THE CAPT SHOULD HAVE STATED TO THE CTLR EXACTLY THE SITUATION WE WERE EXPERIENCING SO THAT ALL PARTIES INVOLVED COULD HAVE WORKED TOGETHER MORE EFFECTIVELY AND SO THAT THE CTLR MIGHT BETTER UNDERSTAND OUR NEED TO DSND IN ORDER TO BRING THE CABIN TO AN APPROPRIATE LEVEL. SUPPLEMENTAL INFO FROM ACN 735502: WE HAD JUST PICKED UP OUR IFR CLRNC WHEN WE NOTICED THE CABIN WAS NOT PRESSURIZING PROPERLY. WE HAD JUST BEEN CLRED UP TO FL280 BUT ADVISED ATC THAT WE WERE GOING TO STAY LOW FOR A COUPLE OF MINS. OUR ALT WAS BTWN 7000-10000 FT. WE ENDED UP DSNDING TO 6300 FT UNTIL WE WERE SATISFIED THAT THE CABIN PRESSURIZATION WAS WORKING PROPERLY. AT THAT TIME CTR QUERIED US ABOUT OUR ALT AND SITUATION. I ADVISED ATC THAT EVERYTHING WAS UNDER CTL AND THAT WE WERE READY TO START UP TO FL280. THE CTLR FURTHER QUESTIONED US ABOUT THE ALTDEV. I TOLD HIM THAT I WOULD RATHER EXPLAIN IT OVER THE TELEPHONE AND REQUESTED A PHONE NUMBER. WE CONTINUED TO ZZZ; CLRED CUSTOMS AND THEN I CALLED CTR WITH THE PHONE NUMBER GIVEN TO ME. I EXPLAINED OUR SITUATION DURING THE FOLLOW UP PHONE CALL. IT WAS EXPLAINED TO ME NO FURTHER ACTION WOULD BE TAKEN. THE ACFT WAS IN VMC CONDITIONS DURING THE SITUATION. ONE MAJOR ISSUE I FEEL LED TO THIS SITUATION IS THAT WE RECEIVED THE CLRNC THE EXACT SAME TIME WE NOTICED THE CABIN PRESSURIZATION ISSUE. (THE PRESSURIZATION PROB CAME FROM CTL SWITCHES IN THE WRONG POS.)