If you were looking for Tinkerer Goblin and have found it inside the Dungeon; try to go deep enough, and you are technically in 'Cavern' layer. However, that was a late find and you might have learned from experience. Numerous players would find him in therelatively less hostile area.
Finding Goblin tinkerer
Once you’ve defeated a Goblin Army, you’ll finally be able to find the famous Goblin Tinkerer. Though it is a bit random and there isn’t much to be done regarding such part. NPCs, similar to monsters, spawn based on the location of your character so lighting is the main thing in order to see when he would spawn. Once you are this deep, you are certainly in the Caverns. Light up the areas and try to fight and summon monsters in order to get loot and cash, and while you do so, Tinkerer Goblin will finally spawn nearby. Ensure there is a spare house back in town so that the player of yours might move in!
The Goblin Tinkerer NPC as mentioned at http://terrariaforpc.com/will only spawn in the layer of Cavern, that’s under the 'Underground'. You can easily guess it when you are getting to Caverns by achange in blocks from mostly stone to mostly dirt and stronger ores. The music would also change along with the background. You will also find depth worms, spiders, and black slimes. You essentially can’t go very deep;however, certain stronger enemies can also spawn at lower levels. Just do not go all the way to Underworld. Try to stay minimum a few screens on lava if it begins to spawn.
Try to work on lighting up an area with help of a number of torches, so that you can see clearly. Tinkerer Goblin could spawn in the corner that’s dark. He certainly will be bound, and you can help him to untie and to free him. You can also hang around same farm and area, and keep roaming to kill and summon monsters. However, Tinkerer Goblin will spawn eventually nearby off-screen, so moving while looking for enemies in order kill and summon them will eventually lead you directly to him.