Data is thin that would confirm that there was ever an actual program referred to as "Pounce", yet there are intriguing bits and pieces to be found in the archives.
Documents circa 1953 reveal stories of F-86 interceptors being vectored toward UFOs, some of which escaped pursuit by exiting vertically, presumably into outer-space. These jet planes had been maneuvered into what was being referred to as "pounce" position. Ground Control Intercept (GCI)had specifically used the term "Pounce Position" when describing, at least one, of the accounts the of F-86 interceptions.
An Internet search conducted on the phrases "air combat + Pounce" took me to several papers dealing with military air combat. Pounce seems to be a fairly common term. It refers to the act of pouncing on a ground target, as in a railroad yard, or bridge, as well it also was used when referring to the act of the pilot getting his plane over, and above an air target. Once they were above the target, and hopefully unseen by the enemy aircraft as well, they would "pounce" upon them in surprise.
The air target grammar usage fits the UFO encounters of 1953, as the interceptors were getting over, and above the UFO targets. As you can see from this web site, others have a slightly different tale to tell, as regards to Project: Pounce.
This is quoted from Ruppelt's whose-who, via NICAP one of the thousands of benefits received from the hardworking folks with NICAP.
Col. Methaney was the CO of the 34th Air Defense Division in Albuquerque. He is now a Brigadier General. He was firmly convinced that the UFO's were real and that they were interplanetary space ships. He wrote up a plan that called for a special squadron of stripped down F-94C's to chase the UFO's. The plan went through Western Air Defense Headquarters and to Air Defense Command Headquarters but it was rejected because of the non-availability of the aircraft. It was in the 34th that the F-86 pilot claimed that he shot at the UFO...Colonel Methany (Ruppelt misspells in these notes but not in his book) was indeed head of the 34th Air Defense Division at Kirtland AFB in Albuquerque, New Mexico. His plan, dubbed Project Pounce, to use F-94C fighters to go after UFOs with gun-cameras was discarded under the motive that due to the Korean war, there were not enough planes available...The UFO shooting incident Ruppelt refers to is detailed in the beginning of Chapter 1 of his book. "
This search is on-going. I will update all other info I find on Project:Pounce