A few random thoughts:
That training base is in a very busy air corridor, and midway between Phoenix and Tuscon. Ton's of aviation of all types. It's also very close to the US ADIZ border. The relevance of that is that is that three aircraft on radar but not accounted for would set off alarm bells in some tower or control center pretty quickly.
Could be bats, but my vote is for birds. The flight arc skirting the runway avoids the big loud helicopter lifting off. (Though having grown up on an USAF base, I'll attest to the fact that birds get accustomed to aircraft very quickly, much to the regret of both types of aviator sometimes.)
Plenty of nocturnal birds indigenous to the region: Nighthawks, nightjars, owls or best yet... goatsuckers (in Spanish that's "Chupacabra".... cue X-Files theme!) The erratic flight pattern wouldn't be odd for juveniles 'playing', mate competition or feeding behavior. (Most feed on insects caught in flight, like bats and swifts, not goat blood.) Citing this bit about the flight pattern of Nighthawks:
"With only a small window of time in which to find food, nighthawks forage continuously on the wing like swifts, swallows and the big brown bats that share the Okanagan's ample insect resources."