Phrase for having nearly completed something

Is there is a phrase for when you're very close to achieving something you've been working on?

When the detective gets that final clue, but hasn't quite solved the mystery yet. When you've done 90% of the work and rest is easily achievable.

I keep thinking it's something like "you can taste it", or "the home straight" but that doesn't quite sound right

Solution 1:

You could say on the verge

a limit beyond which something occurs; brink ⇒ on the verge of ecstasy [Collins]

Alternatives are

threshold: the starting point of an experience, event, or venture [Collins]

and brink: the verge of an event or state [Collins]

A phrase along the lines you mentioned is home stretch

The last part of an activity or campaign [Oxford Dictionary Online]

Solution 2:

You could say the job is "all but finished". It literally means everything has been done except for declaring the job finished, or perhaps performing some finishing touches. Not to be confused with "anything but finished" which has the exact opposite meaning.

Solution 3:

I believe you're thinking of the home stretch:

that part of a race course between the last curve and the winning post.

Webster's Revised Unabridged Dictionary