1650s, "sense of touch or feeling" (with an isolated instance, tacþe from c. 1200), from Latin tactus "a touch, handling, sense of touch," from root of tangere "to touch," from PIE root *tag- "to touch, handle." Meaning "sense of discernment in action or conduct, diplomacy, fine intuitive mental perception" first recorded 1804, from development in French cognate tact. The Latin figurative sense was "influence, effect."
word-forming element meaning "lacking, cannot be, does not," from Old English -leas, from leas "free (from), devoid (of), false, feigned," from Proto-Germanic *lausaz (cognates: Dutch -loos, German -los "-less," Old Norse lauss "loose, free, vacant, dissolute," Middle Dutch los, German los "loose, free," Gothic laus "empty, vain"), from PIE root *leu- "to loosen, divide, cut apart." Related to loose and lease.
<a href="https://www.etymonline.com/word/tactless">Etymology of tactless by etymonline</a>
Harper, D. (n.d.). Etymology of tactless. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/tactless