I can find no definitive source of the phrase “desire line”. It is frequently attributed to Gaston Bachelard’s “The Poetics of Space”, but this appears to be a circular reference, each article citing another with the same untraceable attribution. The book itself contains no mention of the phrase. A search for the origin of a phrase is a desire line of sorts. A circular journey in search of a mythical source that spirals back to where it started.
Not quite a source, but the intriguing Matthew Tiessen both gives his own delightful description of a desire line and references Bachelard’s evocation of desire lines, if not his actual use of the phrase in this wonderful article:
“Desire lines that are about pleasure are less goal oriented, they are less about going from point A to B. These ones meander, they document dilly-dallying, they succumb to the beckoning of the untravelled and unknown. Gaston Bachelard evokes such a desire line when he writes: “We do not have to be long in the woods to experience the always rather anxious impression of ‘going deep and deeper’ into a limitless world. Soon, if we do not know where we are going, we no longer know where we are” (Bachelard, 1964, p. 185).”