Goblin Scout

Scouts do not belong to the invasion even though they look like they do. They spawn during ordinary play, on the surface, in daylight only, and only in the far eastern and western sixths of the map. They will not stand on sand, and they will not stand on ground taken by corruption, crimson or hallow, so the beach itself is usually a dead zone and the clean forest just inland is where they turn up.

Two seeds change that. In Celebration Mk 10 they keep to the surface but stay well clear of the ocean spawn point, and in Don't Dig Up and Zenith they move underground and can appear anywhere in the cavern layer.

They are rare by default, which is the whole difficulty. Breaking a single Shadow Orb or Crimson Heart triples the rate as long as you have not beaten an invasion yet, so do that first and the farming time drops sharply. A Battle Potion with a Water Candle on top is the standard pairing. A Goblin Statue produces them on a wire, which turns the hunt into a switch, and a Lifeform Analyzer will name one before it reaches your screen.

The Tattered Cloth they leave is the piece you cannot get any other way, and it feeds the Goblin Battle Standard that starts an invasion on command. That matters because the invasion is where the tinkerer comes from, and waiting for the game to offer one on its own timetable is far slower than building the banner and starting one the moment your arena is ready.

One quiet tell while you search: get enough of them on screen at once and the invasion music begins playing even though no invasion is running.