Hyphen use?

Kazoo, I'm real solid on this. The way you're using it, "full-length" is a compound adjective--those two words together mean something different than they do separately.

The test is, can you take one away one word and have it still make sense? It's like a blue-ribbon pie or a marriage-minded woman--you can't take away one of the words, because together they mean something different. (Compare to a tall frosty mug of beer or a fast red car--you can remove adjectives and still have something left that makes sense.)

You hyphenate compound adjectives when they come before the noun, and don't if they come after, unless it's needed for clarity. So it's a full-length mirror, but the mirror was full length.

The mixed answers reflect the fact that this can be expressed either way, typically at the preference of the writer.

I would use a hyphen there, but style rules are a bit variable depending on which system you claim to be following, and that is a style issue more than anything.

The main purpose is to eliminate ambiguity as to which word the first one is supposed to be modifying (length or mirror, in this case).  I don't see that it matters a lot which one it is applied to (no possible ambiguity in this particular example) so there is no "need" for the hyphen.  It then becomes a stylistic option.  I simply have a tendency to hyphenate a compound adjective-noun pair such as that, to be certain that there is no misunderstanding (I don't have to verify that I need, or do not need, a hyphen based on what I have written: the pairing decides for me, not the specific context).  I am lazy, I guess.

Imagine, instead, full body suit.  is it a full-body suit, or a full body-suit? or what?

I would use one. This is a specific item. A mirror that is long and narrow. Though sometimes words transition from hyphen to non-hypen. Or into a single word.

Co-operate. Also cooperate. Spell check gives both

yes...............................................

of course it does.

the adjective is "full-length"

you are not talking about a "length-mirror" that happens to be full

please ignore the current fad in (american) English that replaces all hyphens with spaces