Why is Mitzvah compared to a Ner, and Torah to light?
Rashi #1 (from Sotah 21a): Light always illuminates. So Torah's merit always stands for a person. The merit of a Mitzvah is temporary, like the light of a lamp.
Sotah 21a #2: A parable for this is a man walking in the black of the night. He fears thorns, pits, wild beasts, and robbers. Also, he does not know on which path he is walking. If he gets a torch, this saves him from thorns and pits. He still fears wild beasts and robbers; and does not know on which path he is walking. When dawn comes, he is saved from wild beasts and robbers, but he still does not know on which path he is walking. When he gets to the crossroads, he is saved from all his concerns.
Shocher Tov 27: David says, when I begin Divrei Torah, they flow, and when I enter them, many gates are opened for me. Mishnas R. Aharon (4 p.36-37) - when I begin, the light is small, like a lamp. Later, there is great light.
Rashi: A father's command is a lamp - whoever fulfills it, it is as if he takes a lamp in his hand to light it in a dark place. If anything is lost there, he finds it via the lamp's light. Similarly, one who fulfills his mother's instruction, it is light for him - "v'Al Titosh Toras Imecha" (20). (Comment from R. Yosef Kara - Surely this verse discusses his parents' commands! "Mekalel Aviv v'Imo Yid'ach Nero be'Eshon Choshech" (20:20) - if man's lamp is dimmed when he does not fulfill [their] Mitzvos, when he fulfills Mitzvos, it illuminates.)
Malbim: A Mitzvah is particular; it is compared to an individual lamp. Torah is general; it is compared to light, which is encompassing. A lamp burns only as long as there is oil and a wick. So a Mitzvah is only when the [Nefesh] is confined in the body. Light illuminates by itself. The light of Torah clings to the Nefesh, because it is a Divine Neshamah. Also after it separates [from the body], Elokim's light illuminates on their heads and their crowns are on their heads. Just like a lamp illuminates via light, so a Mitzvah guards via engaging in Torah - an ignoramus cannot be a Chasid (Avos 2:5). Light of Torah comes from above, and Ner Mitzvah is from below, in bodily matters tied to the Nefesh.
How is Tochachas Musar Derech Chayim?
Rashi: It tilts a person to life.
Malbim: Even though he has light and a lamp, he must go on the path of life. If not, the light and Ner will not help. What leads him on the path of life? Tochachas Musar. Via accepting Tochachah of Sechel from Musar and Yir'as Hashem, he goes on the path of life. Then, Ner Mitzvah and Ohr Torah guard him from thorns and pits - "Yir'as Hashem Reishis Da'as" (1:7).
