According to Brihat TantrasAra's Pariccheda 2, this Mantra is also found in the Gautamiya Tantram, which is a Vaishnava Tantra.
The Rishi and other limbs of the Mantra (as found in Gautamiya) are quoted in Brihat TantrasAra's page 237.
TathAcha Brihad Gautamiye ----- Bhogamokshaikanilayo luptabijo
Uddharettu prithakatvena kAmavijam mahAmune ||
TadyogAt phalado mantro nAnyathA siddhaye bhavet ||
This verse say that during Puja or while doing the chant the Mantra must first be prefixed with the KAmaBijam (which is Kilm). Only then the Mantra can be mastered and is useful otherwise not.
The limbs of this Mantra can also be found from the following passage:
Shirasi nArada rishaye namaha mukhe virAt chandase namaha hrudi shri
krishnAya devatAyai namaha | Guhye klim bijAy namaha etc...
So, NArada, VirAt and Krishna are respectively the Rishi, Chandah and DevatA of the Mantra as given in Gautamiya Tantram.
The Brihat TantrasAra also states that before doing Japa of the Mantra one is required to do 3 special NyAsas namely - Srishti NyAsa, Stithi NyAsa and Samhriti NyAsa besides doing the other regular ones.
Several related Mantras (like Klim GopijanavallabhAya SwAha etc) are also found in another Vaishnava Text called Sanatakumara Tantram as per TantrasAra.