Not necessary but would be fun...

Gattling Turret: I use the Modular Turrets Mod for base defense (turrets are expensive to produce but blow most other turret mods, including yours out of the water in terms of performance). It includes a Gattling Gun, probably based on the M-134. Compared to the Heavy MG it has shorter range and lower damage but the rate of fire is insane. This makes it ideal for dealing with swarms of small biters, but far less effective against the bigger strains. So it's useful during mid game but becomes wasteful later when small biters are extinct.

Would you be interested in creating a version of it as a weapon pod?

Heard of that mod, but never really downloaded or tried that out, since it seems to be aimed for players playing with hardcore alien mods, which I never tried with.
Maybe you can tell me if those turrets are balanced to vanilla? Like they make the vanilla turrets useless or not? If such turrets on the enemy team (say PvP, or some preset scenarios), how would they perform?

But for now just consider in a vanilla-style game... Against the swarms, it sounds like both the autocannon pod and flamethrower pod propane gas fuel variant are way more effective (as AoE damage) than what a "Gatling pod" could do. So I wonder if it has any real uses?
PS: This Gatling gun sounds highly similar to shotguns in such use. By the time pods are available (together with tanks, grids), shotguns are WAY inferior to other weapons. That's why the shotgun shells are not included in the pod choices.

Damage-wise, probably not balanced to vanilla, but balanced against the HMG in that mod. In theory it would bevas simple as not including or reducing the bullet damage mod to be in line with vanilla. In PvP it would be most effective against light vehicles lightly armored enemies, and be a good area denial tool pre oil. Personally based on scaled and ranges of other weapons in the game, it seems like either flame weapons are op or guns don't have near enough range. My bet is the later more than the former, but it could be a little of both.

Based on your consideration, id say the gattling weapon would be pre autocannon. The technology dates back to before the American Civil War and was used as an area denial / mass killing tool. It kills by weight of fire with a narrow strike area so directly the opposite if a shotgun. Stronger by a bit but far more wasteful so great if you have metal to throw but would be outmoded by mid to late mid game.

Hope that helps. Mostly just feel like its a gap in tech that could be filled.

Before talking about balance (which is the more complicated problem IMO), let's consider the settings first, if Gatling pod is applied:
Both tanks and gun pod 1 techs require science pack 3 (cyan beaker), which needs advanced circuit (red circuit), which needs plastic, which is an oil product.
So as a pre-oil weapon... it becomes inferior at the moment it's available, like a shotgun pod.

Autocannon pod is unlocked by cannon pod 1 tech, which is double the cost of gun pod 1 but not needing extra science packs, so there's not much gap between basic gun pod and autocannon pod. (I would not increase this gap neither, since basic gun pod should only unlock after tanks is available. And autocannon is from the cheapest tank: light tank.)
So as a pre-autocannon weapon... it just appears 1 or 2 tech before autocannon pod.

In both considerations, there seems not enough room for Gatling pod.

Back to the balance problem...
Yes, balance is the most important thing when adding any weapon, from my perspective. Anything new should balance with vanilla weaponry. It is because I don't want to make the WHOLE new balancing by myself. Maybe you can suggest some stats, so I can see if it is balanced.
The vanilla gun turret is OP IMO, when both bullet damage and gun turret damage tech bonus are applied. Especially when come to infinite tech era, the gun turret becomes far too OP from +70% damage every gun turret damage tech (plus bonus from every bullet damage tech). This is not a real issue, however, since vanilla gun turret has a quite short range. Players (at least my experience in vanilla multiplayer servers) just spam the more OP laser turret which has much better range and simpler logistics.
So my question is, is such a gun turret/pod with even shorter range useful in vanilla game?

Difficult to say, really. The first time I even came accross the concept of gun pods was in another mod altogether, and I fell in love with the idea of modifiable vehicles. IRL, the M-134 is mounted on anything from an SUV to a helicopter. You're correct though, since the autocannon is available so early, there is no real room for it in the tech tree. Gattling turrets in Modular Turrets isn't even available until after military3 and electric engines are available. From my perspective the automatic cannon is available much too early. But that might be another conversation.

Looking into Gatling. The classic Gatling guns used by US Army adopted .42 (10.75 mm) to 1 inch (25.4 mm). I guess they are having higher caliber than standard infantry rifles in that era?
Quoting from Wiki, the M61 Vulcan is a hydraulically or pneumatically driven, six-barrel, air-cooled, electrically fired Gatling-style rotary cannon which fires 20 mm rounds at an extremely high rate. And a modern Gatling "GAU-8 Avenger" is a 30 mm hydraulically driven seven-barrel Gatling-style autocannon mounted on A-10. (Actually M61 Vulcan and 2 cm KwK 30 on PzKpfw II are what I have in mind when assigning the autocannon to light tank.)
So I guess they are highly-similar things, and actually in the same gun family? My feeling is having lower caliber, further down to the point of like 9 mm, then it becomes more close to the high rotary speed gun you thought about. When having high caliber 20 mm or 30 mm like in modern Gatling, then it becomes the autocannon.
EDIT: See below...

Well, I searched more and found the following, also quoting from Wiki:
The M134 Minigun is a 7.62×51mm NATO, six-barrel rotary machine gun with a high rate of fire (2,000 to 6,000 rounds per minute) which can also fire at a high sustained rate. It features Gatling-style rotating barrels with an external power source, normally an electric motor. The "Mini" in the name is in comparison to larger caliber designs that use a rotary barrel design, such as General Electric's earlier 20-millimeter M61 Vulcan, and "gun" for the use of rifle caliber bullets as opposed to autocannon shells.
So I guess "Minigun" is what you want, and would be a more exact term in modern military glossary?
Therefore, both minigun and autocannon actually come from the same Gatling mechanism. Caliber is the only meaningful difference between the two.
Technically, minigun is more difficult to make than autocannon, because minigun needs a much higher rate of fire to be effective as lower caliber, causing a lot of overheat and reliability issues. If one of them should be available later, it would be the minigun instead, not the autocannon.

I had actually thought about adding a "Minigun Pod" when this mod was still in development. It was designed to be a 4×4 equipment to justify the boost in range than vanilla gun turret, because vanilla gun turret range is too lame... But then the setting was quite opposite to what you have requested.

Perhaps, but if it's more athuentic, why not?

I did not made that, because I am worried of adding something new but not balanced. Making outer things useless (like vanilla gun pod) is what I tried to avoid. To balance the would-be Minigun Pod, size, rate of fire, damage bonus are nerfed for the range, is it fair?

Here are the specs, together with current gun pod as reference:
Minigun Pod: 4×4, Range 15, RoF 40/s, Damage Bonus +50%
Gun Pod*: 2×2, Range 12, RoF 10/s, Damage Bonus +100%

So for the same size, place for 1 Minigun Pod can have a group of 4 Gun Pod. Minigun Pod would have 75% DPS of the group of 4 Gun Pod, but with better range.
What do you think about these settings?

Looks ok to me. I like the tradeoff. Have you tested it in game? Stats are one thing, but actual performance could vary.

My code is there so played it a bit. I have pods on tanks together with PLD on armor, so actually not much can get close. Minigun pod thinned their group at mid-range and the flamethrower pod with propane gas fuel got biters in closer range. It is hard to tell its difference with gun pods though, without in-depth testing.
The extra range helps killing spitters, like the autocannon pod. Actually the two do very similar thing, as predicted.

I am busy developing a new mod, so do not have time to test it thoroughly with other pod combos and/or upgrade tech bonus. I will come back to this when I have time.

Cool deal. Thanks for all your hard work.

Thanks for making the Miniguns!

Minigun pod (together with Minigun turret in another mod) are here!
But I have to nerf them in damage bonus, when I compare the DPS values with other turrets.

Its fine! Balance away.