You are correct. There is a book near where you found the mirror, between or beside some packages/crates.
You need a pool of water (the large puddle just south east of Goemoe's house). Drop the mirror in the water, and when it disappears, drop in the gem.

BTW, don't tell either healer that you have cured their patient until you have cured both of them.

Check your quest log on this one; it can contain additional hints on what to do next.
Elrath, the Plague and the Poisoned Harvest

Is Tingalf still around? Lt Robin should have had him arrested.