BE400 FLT CREW; CONDUCTING VOR APCH; INITIALLY FAILED TO CONTACT TWR; THEN OVERSHOT FINAL ON APCH. COURSE WAS CORRECTED AND FLT CONTINUED TO LNDG.

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NAV #1 FAIL ENRTE TO TEB. VOR/DME A APCH IN USE LNDG RWY 19. CAPT'S LEG. WITH NAV #1 INOP; CAPT AND FO DECIDED TO HAVE FO FLY THE APCH AND RETURN ACFT CTL TO CAPT WHEN APCH COMPLETED OVERHEAD TEB. IN HINDSIGHT; THIS WAS POOR DECISION MAKING AND WAS LIKELY AGREED TO DUE TO BOTH PLTS BEING TIRED. FO WAS NEARING THE END OF A 14 HR DUTY PERIOD. FO WAS BRIEFED 10 HRS PRIOR TO SHOW TIME; AND BTWN LATE NOTICE AND A NEW BABY; HAD BEEN AWAKE NEARLY 20 HRS; NOT EATEN IN 7 HRS. IN ANY CASE; THE CAPT WAS HANDLING RADIOS AND FORGOT TO CONTACT TWR; AND FO RELINQUISHED CTL TO CAPT OVERHEAD TEB; THINKING THEY WERE AT A POS TO TURN DOWNWIND. FO WAS UNABLE TO SEE THE ARPT. CHKLIST WAS STILL BEING PERFORMED AND CREW TURNED DOWNWIND OVERHEAD; COMPLETING THE CHKLIST. FO NOW WAS PNF AND ASKED CAPT IF HE CALLED TWR. NO REPLY. FO CALLED TWR; WHO WAS ALREADY ASKING US WHAT WAS GOING ON; AND AT THIS TIME; CAPT HAD BEGUN A R TURN TO CORRECT COURSE. IT WAS TOO LATE BY NOW. WE TURNED FINAL; OVERSHOT AND RETURNED TO COURSE; LANDED. THE NEXT MORNING; AFTER CALLING IN FATIGUED (A MINIMUM REST OVERNIGHT WAS ASSIGNED; FO REFUSED); WITH ADEQUATE REST; IT WAS CLR TO US THAT WE CREATED OUR OWN MESS OUT OF A SIMPLE INST ERROR. THIS GOES TO SHOW HOW 2 TIRED PLTS CAN OVER-COMPLICATE WHAT SHOULD HAVE BEEN A ROUTINE FLT WITH A SIMPLE VOR OUT. RECOMMENDATIONS: 1) CALL IN FATIGUED BEFORE YOU DETERIORATE; EVEN IF COMING IN FROM A DAY OFF. 2) WHEN THE COMPANY KNOWS AN EARLY SHOW; WITH A TIME CHANGE IS SCHEDULED; DO NOT WAIT UNTIL THE LAST MINUTE TO NOTIFY A CREW MEMBER.