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.