REPORTER STATES ATC CTLR DID NOT HANDLE REQUEST FOR CONTACT APCH. FLT CREW DEVIATED FROM ASSIGNED RADAR VECTOR HEADING.

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CASTLE APCH CTLR HAD ISSUED HDG 120 DEGS AND 3000' AND TO EXPECT THE ILS RWY 28R APCH. AT APPROX 7 MI FROM THE ARPT ON A LEFT DOWNWIND THE ARPT WAS IN SIGHT AND WAS RPTED TO ATC AND A CONTACT APCH WAS REQUESTED. CASTLE RPTED TFC ON FINAL FOR RWY 28R AT MODESTO. AT FIRST WE WERE UNABLE TO SEE THE TFC AND RPTED NOT IN SIGHT (THE CTLR SEEMED TO BE CONFUSED OR PREOCCUPIED ON THE TERM CONTACT APCH). THE OTHER ACFT WAS THEN SIGHTED AND RPTED IN SIGHT. I AGAIN REQUESTED THE CONTACT APCH. LIKE BEFORE; ANOTHER LONG PAUSE FROM APCH CTL AND THE CAPT BEGAN A LEFT TURN TO FINAL AND I BROUGHT TO HIS ATTN THAT WE WERE TURNING OFF OF OUR ASSIGNED HDG AND ALT AS HE BEGAN HIS DES. THE CTLR THEN SAID CONTACT THE TWR. I CONTACTED THE TWR AND ASKED HIM TO VERIFY THAT WE WERE CLRD FOR THE CONTACT APCH. AFTER A LONG PAUSE HE CLRD US FOR THE CONTACT APCH AND TO LAND. IN SUMMATION; THERE SEEMED TO BE SOME CONFUSION ON WHO WAS SUPPOSED TO CONTACT THE TWR BTWN US AND ATC. CASTLE SEEMED TO BE CONFUSED ON THE TERM OR DEFINITION OF A CONTACT APCH AND MY POSITION AS A NON FLYING COPLT TRYING TO CLARIFY ATC INSTRUCTIONS AND STOP OR BRING TO THE ATTN OF THE CAPT THAT HE IS DEVIATING FROM THE LAST ASSIGNED CLRNC RESULTED IN AN UNCLR SITUATION.