word forming element indicating "oneself," also "automatic," from Old English use of self (pron.) in compounds, such as selfbana "suicide," selflice "self-love, pride, vanity, egotism," selfwill "free will." Middle English had self-witte "one's own knowledge and intelligence" (early 15c.).
OED counts 13 such compounds in Old English. Middle English Compendium lists four, counting the self-will group as a whole. It re-emerges as a living word-forming element mid-16c., "probably to a great extent by imitation or reminiscence of Greek compounds in (auto-)," and formed a great many words in the pamphlet disputes of the 17c.
"lenient, willing to overlook faults," often in a bad sense, "too lenient," c. 1500, from Latin indulgentem (nominative indulgens) "kind, tender, fond," present participle of indulgere "be kind, be complaisant, yield" (see indulgence). Related: Indulgently.
<a href="https://www.etymonline.com/word/self-indulgent">Etymology of self-indulgent by etymonline</a>
Harper, D. (n.d.). Etymology of self-indulgent. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/self-indulgent