The Ancient Factory hides deep underground and never breaks the surface, so finding it by wandering the caves is almost hopeless. The 
Eye of Mech is the answer. This locator item points you straight to the nearest factory, and it later doubles as the key that brings The Harbinger back for another fight.
You throw it like an 
Eye of Ender, but it never breaks and never leaves your inventory when you use it to search. It is also fireproof, so it survives lava if you drop it in the deep caves.
Obtaining
You craft the Eye of Mech at a Crafting Table. The recipe wraps a single Eye of Ender in four 
Iron Ingots and four 
Redstone Blocks. Since an Eye of Ender needs 
Blaze Powder, plan a trip to the Nether before you build one.
One craft gives you a single Eye of Mech, and since searching never uses it up, one is all you need for your entire world. Craft extras only if you plan to respawn The Harbinger repeatedly.
Usage
Finding the Ancient Factory
Hold the Eye of Mech and right-click to launch it into the air. It flies toward the nearest Ancient Factory, hovers for a few seconds to mark the direction, then fades away without breaking or leaving your inventory.
The eye only reacts if a factory sits within roughly 1,600 blocks. If nothing happens when you right-click, travel a few hundred blocks in any direction and try again until it launches. After each successful throw there is a short cooldown of about three seconds before you can use it again.
Respawning The Harbinger
Beating The Harbinger leaves behind a Boss Respawner block in the arena where you fought it. Right-click that block with an Eye of Mech and, after a short charge-up, The Harbinger returns for another fight.
Using the Boss Respawner consumes one Eye of Mech every time. Keep spare Iron Ingots, Redstone Blocks, and Eyes of Ender on hand if you plan to fight The Harbinger repeatedly.
Tips
The Ancient Factory is home to The Harbinger, along with The Prowler and The Watcher. Gear up for a hard fight before you dig in, because these mechanical enemies hit fast and hurt. Bring blocks to seal off tunnels so you are not swarmed the moment you break through.
Bring 
Fire Resistance potions, a 
Shield, and 
Golden Apples before entering the factory. The Harbinger fires lasers that set you on fire and shoots Wither Missiles that inflict the Wither effect. Fire Resistance covers the burns, Golden Apples offset the Wither damage, and a water bucket puts you out quickly after a laser hit.
The fight has two phases. Use a 
Bow from range in the first phase, then switch to a 
Sword once The Harbinger drops to half health and becomes immune to arrows.
EMP pillars stand around the boss arena, each wired to a lever. Pull a lever to unleash an EMP pulse that stuns The Harbinger and opens it up to free hits, but the pulse also hurts anything within about five blocks. Each pillar only fires once, so lure the boss next to a pillar before you flip the lever, and back off as its health reaches zero since The Harbinger explodes on death.
One Eye of Mech finds every factory you will ever visit, so do not waste time crafting spares just to explore. Save extra eyes for the Boss Respawner instead. The Watchers and Prowlers inside the factory drop Iron Ingots and 
Redstone, which covers most of the recipe, though you still need an Eye of Ender for each replacement.
If your first few throws do nothing, you are simply too far from any factory. These structures are rare and spread far apart, so cover real distance between attempts rather than throwing from the same spot.
FAQ
It locates the Ancient Factory. Right-click to launch it, and it flies toward the nearest factory to show you the way. It also acts as the key to respawn The Harbinger at a Boss Respawner block.
No. Unlike a vanilla Eye of Ender, it never breaks and never leaves your inventory when locating a structure. One eye lasts forever for searching. It is only consumed when you feed it to a Boss Respawner.
Place one Eye of Ender in the center of a Crafting Table, surround it with four Iron Ingots on the edges, and put four Redstone Blocks in the corners. This makes one Eye of Mech.
No Ancient Factory is close enough. The eye only detects a factory within about 1,600 blocks, so if it does nothing, travel several hundred blocks and try again. These structures are rare and far apart.
After you kill The Harbinger, a Boss Respawner block appears in the arena. Right-click that block while holding an Eye of Mech to summon the boss again. Each respawn uses up one eye, so keep spares if you want to farm it.
