Learn English – How did the word “important” come to mean “significant”

Equivocal does not mean the opposite of unanimous, nor has it reversed its meaning.

For a person to equivocate is to use ambiguous language, and be non-committal: to "hedge" between two positions without committing to either, and (literally) to "call equally one thing or the other" — to talk equally of two different positions.

Equivocal is the adjective form: an equivocal statement is one which talks equally of two different things, and does not take a clear single position. Unequivocal is the opposite: something with no ambiguity, something that does not equally emphasise two contradicting points, a strong message which leaves no doubt.

Note that these words are generally used to statements coming from one person; they are not (necessarily) related to whether an opinion is unanimous or not. Unanimous just means, as you said, that everyone shares the same opinion. So, when used for a statement made by a committee, all possibilities exist: it may be

• unanimous and equivocal: everyone endorsed a vague statement (most statements by government committees are probably examples)
• unanimous and unequivocal: a strong position that everyone shared
• non-unanimous and equivocal: not everyone agreed with the statement, probably because some of them wanted to pass a clear message instead
• non-unanimous and unequivocal: a strong message that not everyone agreed with.

So you see they are orthogonal, not opposites.

OED to the rescue again...

Etymology: < Latin triviālis, in sense A.5 below, < trivium (see trivium n.); compare French trivial (16th cent. in Godefroy Compl.).

So yes, it comes ultimately from trivium = "three ways", but A.5 says

5. Such as may be met with anywhere; common, commonplace, ordinary, everyday, familiar, trite. Now rare (passing into A.6).

6. a. Of small account, little esteemed, paltry, poor; trifling, inconsiderable, unimportant, slight.

Trivial comes from the Latin trivialis which means very much what trivial does. Quite how the Latin trivialis was derived from trivium is beyond the scope of an English site, but it may well be to do with idle chatter on a street corner.