mid-13c., tohte "stretched or pulled tight," possibly from tog-, past participle stem of Old English teon "to pull, drag," from Proto-Germanic *theuhanan, from PIE root *deuk- "to lead," which would connect it to tow (v.) and tie. Related: Tautness.
word-forming element making verbs (such as darken, weaken) from adjectives or nouns, from Old English -nian, from Proto-Germanic *-inojan (also source of Old Norse -na), from PIE adjectival suffix *-no-. Most active in Middle English and early modern English, hence most verbs in -en are comparatively recent.
<a href="https://www.etymonline.com/word/tauten">Etymology of tauten by etymonline</a>
Harper, D. (n.d.). Etymology of tauten. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/tauten