What is the origin of the phrase "gathering wool"?

It is a very old saying, that dates back at least to the 16th century:

Woolgathering:

• 1550s, "indulging in wandering fancies and purposeless thinking," from the literal meaning "gathering fragments of wool torn from sheep by bushes, etc." (see wool + gather). (Dictionary.com)

Earlest known usages:

• The earliest known use of the phrase in the sense to indulge in purposeless thinking is in The arte of rhetorique: for the use of all suche as are studious of eloquence, sette forth in English (1553), by the humanist and administrator Thomas Wilson († 1581):

  • The reportyng of our tale may soone appere plaine, [...] if we orderly observe circumstaunces, and tell one thyng after another from tyme to tyme, not tumblyng one tale in an others necke tellyng halfe a tale, and so leavyng it rawe, hackyng and hemmyng as though our wittes and our senses were a woll gatheryng.

• To gather wool and to go gathering wool were used in the same sense. For example, in Flovvers of epigrammes, out of sundrie the moste singular authours selected, as well auncient as late writers (1577), the translator and poet Thimothy Kendall (floruit 1572-77) wrote:

  • How the Papist praies. The Papist praies with mouth, his minde on gatheryng woolle doeth goe: Like to a iabberyng Ape, whiche doeth naught els but mumpe and mowe.

(Word history)

From etymonline:

... 1550s, "indulging in wandering fancies and purposeless thinking," from the literal meaning "gathering fragments of wool torn from sheep by bushes, etc.," an activity that necessitates much wandering to little purpose...

Hence it makes the jump from "wandering aimlessly, looking for wool" to any other drifty, purposeless behaviour:

Oxford:

... Indulgence in aimless thought or dreamy imagining ...