John Steinbeck (and following him, the TV series Hell on Wheels) got it wrong: the Hebrew word is actually timshol, not timshel, and it means “thou shalt rule over” or “thou shalt control”—not “thou mayest.”
The context is what God says to Cain (Gen. 4:7), who is disheartened by the fact that God had preferred Abel’s offering of the “firstlings of his flock” over Cain’s offering of “fruit of the ground”:
הלוא אם תיטיב שאת ואם לא תיטיב לפתח חטאת רבץ ואליך תשוקתו ואתה תמשל בו
Halo im teitiv set, ve’im lo teitiv, lefetaḥ ḥatat rovetz,
ve-eleikha tshuqato, ve’atah timshol bo
Although the meaning of timshol is straightforward, the statement itself is obscure, as it appears to have omitted two critical words—yetzer hara (Hebrew, “the evil spirit”)—so what it means is “If you conduct yourself well, [you shall] bear up [well]—and if you do not conduct yourself well, sin lieth at the door—and [the evil spirit] covets you, but you shall manage to control it.”
(Originally written in reply to a question at Quora.com).