Sorry, Guardsman,
Here is more info that might help.
F-101A - Single seat Tactical Fighter version, (special weapons delivery) used by the 27th TFW, Cannon AFB, NM. Aircraft moved to the 81st TFW at Bentwaters and Woodbridge AB in England. Airframe stressed for 6.33 G maneuvers.
F-101C - Single seat Tactical Fighter version. Airframe strengthened for 7.3 G maneuvers. Aircraft to 27th TFW, later 81st TFW. (522nd TFS, 27th TFW sent TDY to Kadena AB, Okinawa in response to the Taiwan Crisis in 1958. Only deployment of the single seat fighter version to the Far East.)
F-101B - Two seat interceptor version. Internal weapons bay for Falcon and Genie air to air missiles. Used by CONUS ADC squadrons, ADC F-101Bs were not based nor sent TDY outside of CONUS. Also used by Canadians.
F-101F - Dual control (flight controls also in the back cockpit) F-101B to be used as a trainer. Used by ADC and some ANG RF-101G/H units. Used by Canadians.
RF-101A - Reconnaissance version stressed to 6.33 G. Used by Tac Recon units in CONUS, and a few were used early in the Viet Nam War by PACAF. (TDY from CONUS? or detached from ROC?) ROC apparently used a limited number.
RF-101C - Recon version strengthened for 7.3 G maneuvers. Used by Tac Recon units in CONUS, USAFE, and PACAF. ROC also used this version.
RF-101G - Conversion of F-101As for Reconnnaissance mission. Used by the KY, ARK and NV ANG. Aircraft sent TDY to Itazuke AB in Japan in response to the Pueblo Crisis.
RF-101H - Conversion of F-101Cs for Recon mission. Used by KY, ARK and NV ANG. Aircraft sent TDY to Itazuke AB.
RF-101B - Conversion of ex RCAF F-101Bs for Recon mission. Used by NV ANG. Did not operate outside of CONUS.
Since ADC did not send the F-101B or F-101F overseas, how did a pair come to be stationed for a year or so overseas? Use as a chase plane is a hint. As far as I know, the TRS units overseas did not operate the two seat trainer version. I don't think that the 81st TFW in England used them either. F-101Bs might have been sent to the Paris Air Show or the one at Farnborough in England.
Sorry, if this is too obscure.
I left it as an aside as it is a pretty obscure question. I did not intend it to be the new trivia question.
It would be a nice beer bet.
Best wishes,
Grant