Old English settan (transitive) "cause to sit, put in some place, fix firmly; build, found; appoint, assign," from Proto-Germanic *(bi)satejanan "to cause to sit, set" (source also of Old Norse setja, Swedish sätta, Old Saxon settian, Old Frisian setta, Dutch zetten, German setzen, Gothic satjan), causative form of PIE *sod-, a variant of root *sed- (1) "to sit." Also see set (n.2).
The intransitive sense from c. 1200, "be seated." The word was used in many disparate senses by Middle English; sense of "make or cause to do, act, or be; start" and that of "mount a gemstone" attested by mid-13c. Confused with sit since early 14c. Of the sun, moon, etc., "to go down," recorded from c. 1300, perhaps from similar use of the cognates in Scandinavian languages. To set (something) on "incite to attack" (c. 1300) originally was in reference to hounds and game.
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Harper, D. (n.d.). Etymology of deep-set. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/deep-set