Mitzvah for an Israelite to Become Impure for a Relative

Is there a mitzvah for an Israelite to become impure for a deceased relative, or is this rule only applicable to Kohanim?

Some deduce from the words of the Rambam that this mitzvah also applies to Israelites and Israelite women. It is proper to be stringent.

The Rambam writes in the Book of Commandments: "Every Israelite is obligated to mourn for his relatives, meaning the five deceased for whom there is a mitzvah. To strengthen this obligation, he explained it with a Kohen, who is warned against impurity, that he must become impure in any case like other Israelites so that the law of mourning is not weakened." From his words, it implies that the impurity of Kohanim for relatives is part of the mourning law, and there is a mitzvah for all Israelites to become impure.

The Ramban writes that the impurity of a Kohen for his relatives is because he is obligated to bury him through the relatives, like a deceased for whom there is a mitzvah, and therefore he is commanded to become impure.