I've always thought that was an electric guitar with a heavy flanger on it, or a synthesizer, perhaps a Moog, or a Farifsa (that's the name of the synth that does light string sounds, right?)
Farfisa is a portable, plastic organ. The light string sounds you're thinking of would more likely be from an ARP String Ensemble.
I've obtained the AFM contracts from those sessions, and among the players is guitarist Dennis Budimir, who is paid for "2 doubles" - leading me to suspect that, in addition to playing guitar on the basic track, he overdubbed extra parts - one of which I would suspect to be a guitar with that "flourish" effect you've described. At any rate, I've long wondered the same as you what specifically is making that sound on those songs, and wondered if it might be a synth. But now I tend to suspect guitar, based on that finding.