uterque

Uterque, utraque, utrumque is uter, "which of two", plus the enclitic -que. It declines like a pronoun: genitive utriusque, dative utrique, and the -que sits on the end unchanged. The verb goes singular, because the sense is "each one of the two taken separately", even where English reaches for a plural.

That is the distinction worth holding on to. Ambo means both together, as a pair; uterque means each of the pair, one at a time. With a personal pronoun it takes a partitive genitive, uterque nostrum, "each of us two". The plural utrique appears only for two groups rather than two individuals, so utrique milites is the soldiers on each side. Latin marks the number two far more carefully than English does, and this is one of the words doing that work.