Midrash sa Exodo 34:21: Mekhilta DeRabbi Yishmael & Mekhilta DeRabbi Shimon Ben Yochai

(Ibid. 3) "You shall not light a fire in all of your dwellings": From (Exodus 34:21) "From plowing and harvesting shall you rest," we derive: Rest from plowing at the time of harvesting, i.e., that one rests from the eve of shemitah to shemitah (i.e., he may not eat on shemitah what he has harvested on the eve of shemitah). I might think that just as he rests from the eve of shemitah to shemitah, so he rests from the eve of Sabbath to Sabbath.

R. Yonathan says: What is the intent of "You shall not light a fire"? From "And Moses assembled, etc.", I might think that one is not liable until he transgresses all thirty-nine proto-labors. It is, therefore, written (Exodus 34:21) "From plowing and from harvesting shall you rest." (I would think that he is not liable) until he transgresses two, and if not, he is not liable. It is, therefore, written "You shall not light a fire."

You shall not kindle a fire - Why is this said? Since it says (Ex. 34:21), "You shall cease from plowing and harvesting", meaning cease from plowing during the harvest and cease from harvesting during plowing. I only know [about the prohibition to work] from the eve of the seventh year to the seventh year, how about from the eve of the Sabbath to the Sabbath? By logic: since the seventh year [sabbatical year] is for the sake of God's name and the Sabbath is for the sake of God's name, if one ceases from the eve of the seventh year to the seventh year, then one should also cease from the eve of the Sabbath to the Sabbath. Another argument: Just as the seventh year, for which one is not liable to court-imposed death, requires one to rest from the eve of the seventh year to the seventh year, the Sabbath, for which one is liable to court-imposed death, should also require rest from the eve of the Sabbath to the Sabbath. Or perhaps one cannot light his lamp, or make a bonfire, or warm his hot water on the eve? The Scripture says, "You shall not kindle a fire in any of your dwellings on the Sabbath day". On the Sabbath day, you shall not kindle [a fire], but you can kindle [one] on the eve of the Sabbath for the Sabbath.
Another interpretation: You shall not kindle a fire - Why is this said? Since it says (Leviticus 6:6), "A perpetual fire shall be kept burning on the altar, not to go out", one might think this applies both on weekdays and on the Sabbath. How then do I fulfill "whoever does any work on it shall be put to death" (Ex. 31:14)? [Is it referring] to all other forms of work except arranging [the wood on the altar], or even arranging [the wood]? How do I fulfill "not to go out" [with the prohibition of work]? Is it on all other days, excluding the Sabbath, or even on the Sabbath? The Scripture says, "You shall not kindle a fire in any of your dwellings". In your dwellings you shall not kindle [a fire], but you can kindle [one] in the Temple.
A student of Rabbi Ishmael said: You shall not kindle a fire - Why is this said? Since it says (Deut. 21:22), "If a man is guilty of a capital offense and is put to death", I might think [the law applies] both on weekdays and on the Sabbath. How then do I fulfill "whoever does any work on it shall be put to death" (Ex. 31:14)? [Is it referring] to all other forms of work except the death penalty imposed by the court, or even the death penalty imposed by the court? How do I reconcile "and he is put to death and you hang him" [with the prohibition of work]? Is it on all other days, excluding the Sabbath, or even on the Sabbath? The Scripture says, "You shall not kindle a fire in any of your dwellings". This refers to the dwelling of the court. Burning was included [in the general prohibition]. Why was it singled out? To draw an analogy from it: Just as burning is one of the four death penalties imposed by the court and it does not override the Sabbath, so too the other death penalties do not override the Sabbath. Hence, penalties are not imposed on the Sabbath.
Rabbi Jonathan says: You shall not kindle a fire in any of your dwellings - Why is this said? Since it says (Ex. 35:1), "Moses assembled the whole Israelite community and said to them, 'These are the things'", I might think that one is not liable unless he violates all 39 primary categories of work. The Scripture says (Ex. 34:21), "You shall cease from plowing and harvesting", or perhaps one is not liable unless he violates two [categories], otherwise he is not liable. The Scripture says, "You shall not kindle a fire". Kindling was included [in the general prohibition]. Why was it singled out? To draw an analogy from it: Just as kindling is one of the 39 primary categories of work and one is liable for it individually, so too for the other 39 primary categories of work, one is liable for each one individually.
Rabbi Nathan says: You shall not kindle a fire in any of your dwellings - Why is this said? Since it says (Ex. 12:16), "But whatever everyone needs to eat, that alone may be prepared by you", I might think that one is not allowed to light his lamp or make a bonfire or warm his hot water [on the eve of the Sabbath]. The Scripture says, "You shall not kindle a fire in any of your dwellings on the Sabbath day". On the Sabbath day, you shall not kindle [a fire], but you can kindle [one] on a festival.