The obvious template for my cover of this probably by-now-iconic piece of soundtrackery is Verlaine's Warm & Cool album, which was roughly contemporaneous with Twin Peaks anyway and definitely explored the same noir territory, but with the bonus of stingray guitar sounds that share a similar lineage anyhow, and which Verlaine had been exploring as his "roots" as far back as the instrumental "The Blue Robe" on his second solo LP Dream Time.
And if you don't care about any of this shit, go ahead and get yourself a copy of Dream Time anyway, because it's one of the best rock and roll albums ever recorded and consistently overshadowed by the records Verlaine made with Television. If you do care about some of this shit, and you like what I did to this piece, but still don't know anything about this Verlaine guy, I still guarantee you'll like Warm & Cool.
But me, I really like Tom Verlaine. He's who I had instead of Jim Morrison, to what I still maintain to have been my advantage.