DURING DEP CLB AN SF34 FLC OVERSHOT ALT WHILE LOOKING FOR TFC. THEY HAD RECEIVED ADVISORY OF 2 TARGETS. FLC RPTS THAT A CONTRIBUTING FACTOR WAS THE DISTR OF THE MASTER CAUTION AND CHIME AND FLASHING R OIL BYPASS LIGHT THAT WAS ON THE MEL. ALTDEV ALT OVERSHOT.

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EARLY AM DEP DELAYED DUE TO ACFT MECHANICAL PROB (DELAYED AT RWY). RETURNED TO GATE. WHILE HAND FLYING ACFT DURING CLB; FLT DIRECTOR ON; EXCEEDED ASSIGNED ALT BY 490 FT. I WAS TIRED; 2 ACFT WERE BEING CALLED AS TFC. BONANZA; AT 12 O'CLOCK AND 3 MI; AND NAVAJO; 1 TO 2 O'CLOCK; 8000 FT AND 2 MI. ALSO THE COCKPIT MASTER CAUTION CHIME; LIGHT AND R OIL BYPASS LIGHT WERE ACTIVATING ABOUT EVERY 10-20 SECONDS REQUIRING ATTN. BECAME FIXATED LOOKING FOR 1 TO 2 O'CLOCK TFC AT 8000 FT. OUR CLRNC WAS TO 6000 FT AND OUR PREVIOUS CLRNC HAD BEEN TO 10000 FT; I STILL HAD 10000 FT IN MY MIND; AS OUR ASSIGNED ALT. PASSING 6300 FT ALT ALERTER WENT OFF; CHIME AND LIGHT. I LOOKED AT THE ALTIMETERS 6300 FT AND THEN THE ALT ALERTER. I IMMEDIATELY LEVELED AND DSNDED TO 6000 FT. NO CONFLICT. I SHOULD HAVE BEEN MORE ALT AWARE; MORE FOCUSED; AND BEING TIRED AND LOOKING FOR TFC; I SHOULD HAVE HAD THE AUTOPLT ON. SUPPLEMENTAL INFO FROM ACN 330350: OUR 1000 FT CALL WAS MISSED AND THE 100 FT CALL WAS MISSED. AT 6300 FT I NOTICED OUR DEV. IN RETROSPECT; THE OIL BYPASS LIGHT CAUSED A MAJOR DISTR IN THE COCKPIT. IT WENT OFF NO LESS THAN 200 TIMES THROUGHOUT THE FLT. WE THEREFORE HAD A TOTAL OF 3 THINGS COMMANDING OUR IMMEDIATE ATTN DURING THE CLB PHASE. A MASTER CAUTION CHIME; TFC AT 10 O'CLOCK AND 1 O'CLOCK.