This is described in the game as:

Improves your mobility.

You can pick this up in eastern Pucara province, at Pilca Mine. There are some enemies around the mine entrance. The accessory case is inside the mine on a table in the room at the end of the mine shaft.

You can try to sneak into the mine shaft here, but it’s a lot easier to at least take out the enemies nearby first, including a sniper in a tower and some patrolling outside. As usual, this is also easier to approach at night when the bodies are harder to see, and some of the enemies will be congregated at a dinner table.

The short barrel essentially makes it easier for you to manoeuvre while aiming so you’re less sluggish, while sacrificing some range and accuracy. Conversely the long barrel does the opposite, giving your gun more range and accuracy but making it more sluggish to move.

I’d say you probably want the manoeuvrability on an SMG and the range on a sniper rifle, but – as with an AR – on an LMG it depends a lot on your play style.

If you run and gun with an LMG, shooting closer targets, then you may want to give the short barrel a try. If you keep your distance then it might be worth picking up the long barrel instead (available in Barvechos).