C560 CREW HAD TRACK DEV DEPARTING TPA.

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TAXIING TO THE RWY FOR TKOF WE WERE DOING THE STANDARD TKOF CHKS. INCLUDED WAS THE TKOF CREW BRIEF DESCRIBING EMER AND NORMAL SOPS WHICH I GAVE AS THE PF. I ASKED THE PNF (CAPT) IF THERE WERE ANY SPECIFIC INSTRUCTIONS FOR DEP SINCE HE HAD THE CHARTS IN FRONT OF HIM. HE DOUBLE-CHKED IT AND SAID NO. UPON RECEIVING OUR TKOF CLRNC NO HEADING INSTRUCTIONS WERE GIVEN. I QUESTIONED THE CAPT ON PROC AND HE SAID WE SHOULD JUST TURN ON COURSE. SHORTLY AFTER TURNING FROM THE 360 DEG RWY HEADING TO 330 DEGS ON COURSE; ATC CALLED US QUESTIONING OUR HEADING. WE REPLIED THAT WE HAD TURNED ON COURSE SINCE THERE WERE NO INSTRUCTIONS ON THE SID. HE TOLD US TO CHK AGAIN. WE DID AND REALIZED THAT THE SID DID STIPULATE FLYING RWY HEADING AFTER TKOF. WE APOLOGIZED AND TURNED BACK TO RWY HEADING. THIS COULD HAVE BEEN AVOIDED IF BOTH PLTS HAD LOOKED AT THE SID CHART TO BACK EACH OTHER. ALSO IF GIVEN A TKOF CLRNC WITHOUT HEADING INSTRUCTIONS BE SURE TO QUESTION THE CTLR TO ELIMINATE ANY CONFUSION AS TO WHAT IS EXPECTED. SUPPLEMENTAL INFO FROM CAN 492006: I WAS CAPT ON A C560 GOING FROM TPA TO FTY. I MISBRIEFED THE SID. I OVERLOOKED THE SECTION WITH HEADING INFO. SUBSEQUENTLY; WE WERE ON THE WRONG HEADING. DEP NOTIFIED US OF OUR DEV. WE CORRECTED HEADING. THERE WERE NO TFC CONFLICTS. ALTHOUGH; THE POSSIBILITY WAS THERE. THE CAUSE OF THE PROB IN MY OPINION; WAS MY LACK OF READING AND BRIEFING THE SID CORRECTLY. CORRECTIVE ACTION ON MY PART; SO THAT THIS WON'T HAPPEN AGAIN IS TO SLOW DOWN A LITTLE MORE AND BRIEF MORE CORRECTLY.