The plane that Hammer was flying was an F-4B Phantom of VF-74. VF-74 made 13 deployments aboard USS Forrestal (CVA/CV-59). One of those was during Forrestal's only WestPac deployment from 6 June - 15 September 1967. While a bit blurry, it is possible to see that USS Forrestal was painted on the side of the plane.
USS Ticonderoga (CVA-14) made a WestPac deployment from 28 Dec 1967 - 17 Aug 1968. Thus it would have been impossible to have been off of Vietnam on 12 Aug and still return to the states on the 17th. Also, Ticonderoga never had an F-4 squadron. Through her career she carried many types of fighters, but never the F-4 in any of its variations. During the time frame that JAG gives for Lt. Harmon Rabb, Sr. flying off of Ticonderoga, Tico's fighter squadrons were VF-191 and VF-194 flying F-8E's, VF-111 flying the F-8H and VF-162 flying the F-8J. All of these are variants of the F-8 Crusader.
VF-53 was assigned to Carrier Air Wing 5 (CVW-5) and was deployed to Vietnamese waters aboard USS Ticonderoga three times: 3 January to 15 July 1963; 14 April to 15 December 1964 and 28 September 1965 to 13 May 1966.
VF-53 was deployed aboard USS Hancock from 5 January to 22 July 1967. On 25 March 1967, a squadron F-8E crashed at sea on a non-combat mission, the pilot LT(jg) James Hise was killed in action, body not recovered.
VF-53 was deployed aboard USS Bon Homme Richard three times: from 27 January to 10 October 1968; from 18 March to 29 October 1969 and from 2 April to 12 November 1970. On 29 July 1968, LCDR Guy Kane flying an F-8E shot down a Vietnam People's Air Force MiG-17.
VF-53 was deployed aboard USS Hancock from 5 January to 22 July 1967. On 25 March 1967, a squadron F-8E crashed at sea on a non-combat mission, the pilot LT(jg) James Hise was killed in action, body not recovered.
VF-53 was deployed aboard USS Bon Homme Richard three times: from 27 January to 10 October 1968; from 18 March to 29 October 1969 and from 2 April to 12 November 1970. On 29 July 1968, LCDR Guy Kane flying an F-8E shot down a Vietnam People's Air Force MiG-17.