The Gunsmith is somewhere in Sakai, but where are they?
Assassin's Creed Shadows features a unique system for tracking quests. After tracking a quest, you receive detailed directions on where to go and you can send a Scout in the area to pinpoint your target. However, not even the Scout gives you the exact location, only a general quest area. This can make it difficult to find certain NPCs in Assassin's Creed Shadows, such as the Gunsmith in the Searching Sakai quest.
The Gunsmith is located somewhere in the large city of Sakai and you need to find them in order to progress the main story. While you can search the entirety of Sakai looking for the Gunsmith, why not just take a look at our guide below to see their exact location?
Gunsmith location in Assassin's Creed Shadows
If you used a Scout to see the general area of the Gunsmith, you'll see the target is on the eastern side of Sakai, in the Firearm District. Though this does make sense, the Firearm District has a ton of small roads and houses to navigate through. This makes it difficult to know where you've already looked, which can result in backtracking and going around in circles looking for the Gunsmith.
Fortunately, you can see precisely where the Gunsmith is located by looking at the map screenshot below:

As you can see, the Gunsmith is located right in the center of the Sakai Firearm District. When you go to this area on the map, you'll have to be stealthy. There are two Gunsmiths talking in the center of a ring and you need to eavesdrop on them by hiding behind a corner nearby. If you don't stay stealthy, though, you won't be able to eavesdrop and progress the quest.
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Completing the Searching Sakai quest in Assassin's Creed Shadows
After the Gunsmiths conclude speaking with each other, you're able to confront them. The easiest way to progress through the dialogue is to select the options with the scales of justice icon on them (looks like a fancy "T"). One point in the dialogue has two scales of justice options, one that says you know the Imai's son and the other that says you know the Imai's daughter.

You want to select the option that says you know the Imai's son, as this makes the Gunsmiths believe you more. However, it doesn't change much in how the dialogue concludes.
At the end of the the dialogue, you can either offer to pay the Gunsmiths for their information or choose to attack them, which results in Naoe chasing after one of them in the streets of Sakai. Either way, you can get what you came for and progress the Searching Sakai quest in Assassin's Creed Shadows.