Two of the best-known candle-lighting customs are the Chanuka lights and the candle by which we search for chametz on Pesach eve.
On the face of it these two mitzvot could not be more opposite. The candle at Pesach eve is entirely utilitarian, in order to help us find chametz, and its entire character is determined by the need for usefulness: if it is too big, the seeker may fear starting a fire, if it is from tallow he may fear soiling his dishes, if it is an oil lamp it may spill, etc. (SA OC 433).
By contrast, the Chanuka lights are entirely anti-utilitarian; it is forbidden to benefit from their light (SA OC 672), and the entire character of the mitzva is determined by this fact: The lights have to be separate so that they won’t appear like a torch; it is preferable for the lights to be low so that they are not useful (OC 671); an extra candle (the shamash) is lit so that any use will by its light only (OC 673), we customarily don’t light the candles one from another (OC 674), and so on.
Yet the Sefat Emet draws a likeness between these two mitzvot. The likeness is based on the Scriptural source which the gemara finds for the candle- light search on erev Pesach:
Rav Chisda said, we learn finding from finding, and finding from seeking, and seeking from seeking, and seeking from candles, and candles from candle. Finding from finding: Here it is written “Seven days leaven will not be found in your houses” (Sh’mot 12:19), and there it is written “And he sought beginning with the oldest and ending with the youngest, and [the goblet] was found” (B’reishit 44:12). And finding from seeking from itself [the verse begins "And he sought"]. And seeking from candles, as it is written “At that time I will seek Yerushalayim with candles” (Tzefania 1:12). And candles from candle, as it is written, “The candle of Hashem is the soul of man, which searches all crevices of the innards” (Mishlei 20:27).
The Gemara goes on to explain that the last verse clarifies that the candlelight search is not a less thorough one seeking with candles instead of a torch to overlook minor transgressions, but rather a more thorough one, just as the lone candle of the soul of man illuminates and penetrates all his innermost parts (Pesachim 7b).
The Sefat Emet explains that the Chanuka light is also meant to help us with a search, but it is an inner search:
For the meaning of the Tabernacle and the Temple is found in every person of Israel as well, as it is said: “And I will dwell within them”. [The term betocham is usually translated "among them", but the Sefat Emet understands it to mean "within them", a grammatically appropriate rendering.] And this is to the extent that a person clarifies to himself that all of his vitality is from the soul… there is a pure point in every person of Israel, but it is hidden and stored away. But when the Temple was in existence it was revealed that all vitality was from God; and this is the significance of the indwelling of the Sh’china (the Divine Presence), a testimony that Hashem dwells among Israel. But now that the Tabernacle is hidden, even so it can be found by searching with candles.
This is the parallel from the Gemara in Pesachim, which explains that we seek Yerushalayim with candles. We seek within ourselves the unique holiness which was revealed then in Yerushalayim, with the help of the Chanuka candle.
The Sefat Emet goes on to explain that just as the actual light of the Temple was lacking in the time of the Maccabees, but miraculously the light was sustained as a testimony to God’s presence, so nowadays we have special Divine aid to find God’s presence within us with the help of the Chanuka lights, which bear a glimmer of the original miraculous light. (Sefat Emet, Chanuka 5631, second night)