leil shimurim and the mitzvah of bitachon

The Torah describes the first night of Pesach as "leil shimurim" (12:42) which Rashi explains to mean that Hashem was watching and waiting for this night (like the expression "v'aviv shamar es hadavar") to fulfill the promise he made to Avraham to redeem his children from slavery. Much has been written on the topic of why it is significant to mention that G-d fulfills his promise when we would expect no less of our fellow man. R' Yerucham Lebovitz in Da'as Torah goes a step further. R' Yerucham asks why it was necessary for G-d to make that promise in the first place. G-d might simply have enslaved the Jewish people and when the proper time came redeemed them. What is the point of making a promise, waiting expectantly to fulfill that promise, and only then acting?

R' Yerucham answers that the purpose of the promise is not for G-d's sake, but for our sake. Through our waiting and hoping with G-d for the promise's fulfillment we generate the merit which leads to that promise coming to fruition.

There is no mitzvah of bitachon (according to most Rishonim) mentioned in the Torah -- where do we derive this midah from? I think the answer is in this vort from R' Yerucham. The midah of bitachon stems from the obligation of v'halachta b'derachav, to imitate G-d's midos, mah hu... af atah... G-d in this parsha demonstrates that he waits expectantly for the fulfillment of his promise; therefore it behooves us to imitate that behavior and also wait expectantly for G-d's promises to come to fruition.