The Watcher Amulet is a Sentry-type Summoning Weapon that spawns a stationary eye at a cursor place which sends out damaging projectiles similar to the Nebula Arcanum's projectile. Those projectiles do not go through blocks.
In order to move the eye around, you need to dispel the Sentry-buff inflicted on you first, then use a weapon again at a different place.
Just like with the Otherworldly Amulet, having the item in your inventory will add a new item to an NPC shop, in this case, the Young Brewer will begin selling the Flask of Rainbows for 1 Platinum.
