Although not at all immediately obvious, 'Pulk/Pull Revolving Doors' evolved out of another attempt at recording 'True Love Waits' in early 2000. When crafting the track, the band went back 4 years and used loops that had been recorded for 'True Love Waits' during the OK Computer sessions in 1996. That isolated session track, called 'True Love Tape Loop', was released in 2017 as a standalone piece on the cassette that was part of the OKNOTOK 20th anniversary release of OK Computer:

The track was thus built from this and other loops, resulting in amost unusual version of 'True Love Waits', which would ultimately be released in 2021 on Kid A mnesia. The track presented here was assembled from stems inside the files of the Kid A Mnesia Exhibition.

In the end, the band did not regard this piece of work as appropriate for 'True Love Waits', but liked the track well enough to keep experimenting. For the new direction the song was to take, Thom apparently turned to the children's encyclopedia series "Childcraft" for inspiration, specifically the "How Things Work" volume. The lyrics of this track can be found in this book to a large degree. There is a section focused on doors, prefaced with a poem entitled "There's More to a Door Than You Think". The lines "there are doors that open by themselves" and "there are doors that let you in and out, but never open" come from different pages in the same section of the book:

Keen to keep things as experimental as possible with this track, Thom decided to go for a similar route for the vocals as with the song 'Kid A' - he didn't actually sing the lyrics, but merely recited them. Where on 'Kid A' melody was created by feeding Thom's voice through the ondes Martenot, it was manipulated for 'Pulk/Pull Revolving Doors' using AutoTune, a program mainly used to correct the pitch of vocal performances. Applying its most extreme mode of correction, it was given a key and then searched for appropriate tones in Thom's talking, thus creating a sort of melody.
The Kid A Mnesia Exhibition contains a stem of the vocals but with no AutoTune applied. This also contains a few lines from the poem that were not included in the final track.

Colin: "'Pulk/Pull Revolving Doors' was made using an MC505 and some loops, together with some other found loops that we made in St Catherine's Court when we were recording OK Computer."

Ed O'Brien: "Nigel was really good because he said... We had this thing at the beginning of the year, and Jonny apparently didn't enjoy these two weeks, but Nigel said like 'Alright, let's split up into two groups'. And we had two weeks of sort of workshop experimental stuff. Nigel said the rules were nobody was allowed to play drums, nobody was allowed to pick up a guitar, the only thing that could be used were sort of electronic, you know, computers, synths, etcetera, etcetera. And it was really good fun. Twenty percent of it was good and the other eighty percent of it was utter rubbish." [...]

Paul Anderson: "Was much of it used, from that, those experimental stages?"

Ed: "Bits... I mean, there's one track that's possibly going... that will come out next year. No, but not a lot."

Thom: "I had this thing for a while where I was falling through trapdoors all the time, into like, acid flashbacks. I'd be talking to someone and then I'd be falling through the earth, and it went on for months and months, and it was really weird. And that was all happening towards the end of OK Computer. And that was all linked in with death. Seeing people dead, like, as I'm talking to you... It's okay," he says reassuringly, looking at my shocked face. "I'm better now."

Q: "I thought, on the new album, on "Amnesiac", track 3, to me, has almost an industrial..."

Colin: "Yeah, 'Push/Pulk Revolving Doors'."

Q: "...hip-hop feel to it. Do you feel that in that track, a little bit of a hip-hop influence, almost, or."

Colin: "You know, it's stuff that we all listen to and that we're into. It was a wide range of tastes. What's cool about that track is it's a sequence that Thom did on the drum machine, basically, together with sounds that we were working on when we were doing OK Computer, like piano and Rhodes put together with a really cool treated vocal. It's a good combination of things there from several years of work. That song is my favorite track, I think."

On Amnesiac, the dirty 808 bass of 'Pulk/Pull Revolving Doors" invites you to reimagine Yorke's mid-80s adolescence - not pining indoors to REM's Murmur and The Smiths' Hatful Of Hollow, but spraying graffiti and breakdancing in deserted shopping centres alongside LFO.

[...]

Another vocal treatment Yorke resorted to was the Autotuner, most famous from Cher's 'Believe', but widely used in contemporary R&B as an intermittent glister of posthuman perfect pitch added to particular lines or words. "We used Autotuner on Amnesiac twice. On 'Packt Like Sardines', I wasn't particularly out of tune, but if you really turn up the Autotuner so it's dead in pitch, it makes it go slightly..." he makes a nasal, depersonalised sound. "There's also this trick you can do, which we did on both 'Packt' and 'Pulk/Pull Revolving Doors', where you give the machine a key and then you just talk into it. It desperately tries to search for the music in your speech, and produces notes at random. If you've assigned it a key, you've got music."

This piece of artwork appeared in the Dead Children Playing book that accompanied the exhibition of artwork that Stanley held at Iguapop Gallery in Barcelona in 2006 (click image for full size):