ACR Y HAD LTSS FROM ACR X ON GAR. SYS ERROR.

Narrative

THE ACTUAL OPERROR AND RESULTANT LOSS OF SEPARATION OCCURRED WHEN THE TWR ADVISED ME; AT THE DEP HDOF POS; OF A GAR ON ACR X BEHIND A PRECEDING DEP ACR Y. ACR Y PRECEDING DEP WAS INADVERTENTLY GIVEN A VECTOR TO THE SAME HDG AS ACR X WAS ON; WHEN THE 2 ACFT WERE ONLY 1 MI APART. THIS RESULTED IN THE LOSS OF THE TWR ESTABLISHED COURSE DIVERGENCE; AND A LOSS OF SEPARATION. AFTER LISTENING TO THE TAPES OF THE INCIDENT; IT WAS DISCOVERED THAT THE TWR HAD ADVISED ME NOT ONLY OF THE GAR; BUT THAT THE GAR WOULD BE HDG 090 DEGS. I DIDN'T HEAR THIS INFO; AND SO I DIDN'T PASS IT ALONG TO THE DEP CTLR. WHEN THE DEP CTLR HEARD ACR Y CHK IN; HE TURNED HIM ON AN INITIAL ON COURSE HDG; WHICH WAS THE SAME AS THE GAR ACR X. THIS CAUSED THE LOSS OF SEPARATION. THE REASON I'M SENDING THIS INFO TO YOU IS NOT SO MUCH WHAT HAPPENED; AS WHY. ON THIS DAY; I STARTED TO FEEL SICK AROUND XX00 AM AND MADE A REQUEST FOR SICK LEAVE AT XX50 AM. THE AREA MGR DID NOT APPROVE MY REQUEST; AND INSTEAD ASKED ME TO REMAIN ON POS FOR 1 HR. I DID AS HE ASKED; THEN ASKED TO BE RELEASED ON SICK LEAVE AGAIN -- 3 MORE TIMES! DUE TO OUR FACILITY'S CURRENT; AND PAST SHORT STAFFING SITUATION; MY SICK LEAVE WAS NOT APPROVED UNTIL XY PM. THIS OPERROR OCCURRED AT XZ AM; A LITTLE OVER 2 HRS AFTER MY INITIAL SICK LEAVE REQUEST. I FEEL THIS SITUATION COMPROMISED THE SAFETY OF THE OP.