The William Tell Fighter Weapons & Air Defense meet competitions are famous from the early 50s.
During the operational period of the F-104 in the USAF also this aircraft participated in some of the meets and even won the 1962 episode (by 479TFW, George AFB).
Known participations include:
September 1959 - Air Defense Meet
The 337th FIS and 538th FIS both participated with a number of F-104A Starfighters. Aircraft seen during these event at least were: F-104A 56-847 and 56-876.
The Larson based 538th FIS also won one of the prices as can be seen on the picture beneath thanks to Andrew Hanna. Only 3 pilots could be recognized by reading their name tags. They are Homer C. Boles, Eustace Mel Bunn and Einar Knute Enevoldson. Who recognizes the other guys?
September 1962 - Fighter Weapons Meet
Nr 479th TFW from George AFB participated with a number of F-104C Starfighters and won the competition.
Aircraft seen were: F-104C 57-914, 57-915 and 57-916. Overall winning F-104C pilot was USAF Captain Charles "Chuck" E. Tofferi.
Beneath a photo taken at Nellis AFB of 57-914 during the Fighter Weapon Meet, taken on September 15th (USAF, thanks to Peter Mühlböck)
Nice video around this 1962 meet can be found here:
September 1963 - Air Defense Meet
Nr 151st FIS participated with a number of F-104A and at least one F-104B Starfighters.
Aircraft seen were: F-104A 56-823, 56-882 and F-104B 57-1302.
September 1965 - Air Defense Meet
Nr 319th FIS, based at Homestead AFB participated with a number of F-104A Starfighters.
Capt J.D.Dunn (319FiS) was declared "William Tell Top Gun".
Likely also in 1960 the 479th TFW participated but we are checking for evidence.
See also video regarding this exercise (including some shots on 319FiS Starfighters, here: