The cover for the single is itself a parody of the Presidents of the United States of America's logo. This is one of Yankovic's shortest album parodies, second only to his remade version of "My Bologna" (a parody of The Knack's "My Sharona"). In the video for this song, Yankovic dons a bald cap. The The Presidents of the United States of America themselves praised the parody and has since often referred to the "Weird Al" song during live performances.
The song was recorded on January 3, 1996 at Santa Monica Sound Recorders, in Santa Monica, California. Before "Gump" was officially released, Yankovic played a rough version of the song for the Presidents of the United States of America on their tour bus. This marks the first time that Al was able to "see a band's reaction when they heard their parody for the first time." PUSA frontman Chris Ballew said he first heard Yankovic was doing his song on television, and later became friends with the parodist. Yankovic even directed a music video for the band's song "Mixed Up S.O.B." in 2008, and has joined them on stage a few times.
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The music video for "Gump" is a double parody of both the movie Forrest Gump and the Presidents of the United States of America's music video for "Lump". The single's cover art is directly taken from the video shoot.
The video begins with a feather blowing through the air, much like the beginning of the original movie.
Throughout the video Forrest offers different people chocolates. He first offers Gladys Ormphby (Ruth Buzzi's Laugh-In character) some chocolates and she hits him with her purse. The second offer is to large, strong man Henry Reichenbach which results in Gump being spun around by his head. He then offers Pat Boone some chocolates. Boone greedily devours most of the box.
The instruments used in the song are over-simplified as a parody of the Presidents of the United States of America's actual instruments (a basitar, or 2 stringed guitar for bass, and a guitbass, which is a 3 stringed guitar). Al uses a one stringed bass in the video, while the guitarist uses a two stringed "guitar".
During the lyrics "He's kind of square", Yankovic makes a square with his hand that appears on screen in dotted lines. This is a reference to Pulp Fiction, a film made the same year as Forrest Gump.
In the instrumential break of the song, it shows Forrest running (a parody of the scene where Forrest runs all around the country) across the street, in a horse race, and outer space. As he runs in the street again, he suddenly bumps into a pole and falls down to the ground, as the song says, "Run...stop!"
As mentioned before, half of the music video is also a parody of the "Lump" music video: Instead of singing in a bog/marsh, Al and his band are dancing in the water fountain in the middle of the park. The silhouette scene in the Lump music video is also parodied, with Al and his band making hand shadows against the background.
Gump is digitally edited into existing footage tapping John F. Kennedy on the shoulder, standing behind Richard Nixon and waving to the camera, and roasting hot dogs at an atomic bomb drop, just like the movie which edited Gump into several newsreels so he appeared to be interacting with historical figures.
The song ends with, "And that's all I have to say about that", which is the way Forrest Gump often ends his stories. Afterwards The Presidents Of the United States of America followed Weird Al's example and ended performances of "Lump" with that quote and they still continue to do so.