The song's music video was the first one released to promote Gordon and was the band's second overall after "Lovers in a Dangerous Time". Like "Lovers", "Enid" was directed by Toronto-based filmmaker Tim Hamilton, who has also directed videos for Rheostatics ("Aliens"), Meryn Cadell ("Inventory") and Ottawa-based rap group Organized Rhyme ("Check the O.R."), which featured a pre-fame Tom Green.
The video features the band playing in a large room themed around the red, white and blue rubber balls that served as the band's logo at the time. Scattered around the room are numerous television screens displaying footage of the band playing outdoors in various locations in Toronto (including Kensington Market).
- The song was the most popular single from Gordon, reaching #2 on the RPM 100 Chart for two weeks in October 1992. It was kept out of the top spot by Patty Smyth and Don Henley's "Sometimes Love Just Ain't Enough". 
- The song's title was inspired by Enid Egars (called Enid Leger by some sources; this may be a mistake or a former name), a waitress at Spanky's Pub in Moncton, New Brunswick whom Ed and Steve had met while touring with Corky and the Juice Pigs. Enid was interviewed about being the band's namesake in celebration of Steve performing a solo show in Moncton in May 2017, almost 25 years after Gordon was released. 
- According to Steve in the liner notes for Disc One, the song's intro in which a radio is heard tuning into a strange Depeche Mode-like song, was achieved by the band building an actual miniature radio transmitter in the studio and recording their own broadcast. The snippet itself was sung by producer Michael Phillip Wojewoda.
- The distinctive squeaking sound in the song (heard most prominently in the intro) is that of a cuica, a type of friction drum originating in Brazil; sound is produced by rubbing a wet cloth on a bamboo rod attached to the drum skin while altering the tension of the skin with the other hand to produce different pitches. Andy can be seen playing one briefly at the end of the video.