[RPG] In Pathfinder, does the summoner or the GM control the eidolon

Problem: Too Many Toons

This isn't really specific to summoners and their eidolons - this is a common issue with anyone who has "other people" along - followers, intelligent familiars or companions, even just random unaligned NPCs like adventure paths like to saddle parties with. I've played Jade Regent and am playing Wrath of the Righteous and in each you end up with a bunch of NPCs in the party that require some spotlight time, and especially in combination with a large group it requires some handling.

Heck, it's even a problem with large parties of only PCs - just too many people spouting words and too many rolls eating up time. That last issue is addressed in How do I run a game for a larger group? but unfortunately most suggestions there are more "split the group"-ey.

Not The Problem: He's My Buddy

The part about him pretending his eidolon is just a buddy (assuming they can conceal the summoner/eidolon "mark" or explain it away as "we got matching magical tramp stamps on spring break in Varisia") is completely legitimate and they need to just get over that (in Sarkoris they believe eidolons are actually gods; varying explanations/cover stories/etc of eidolons are good story diversity). But more to the point it's irrelevant to flow issues.

Limit NPCs

GMs can and should oversee addition of "minion heavy characters" to alleviate this from happening - I've seen groups where every single PC ends up having various followers and summons and whatnot and it's really hard to manage. Especially if there's already 6 or so PCs as well; even if they are only "half a PC" it starts to push the game over the easy-flow threshold. So it's OK to set table rules about it and vet those kinds of PCs. One extra is well within the scope of reason though.

Be Efficient With Their Handling

Then, just have that discussion with the player - ask them to make sure they are being extra efficient. "Roll for both of you quickly, be Johnny on the spot so you're not taking double the time of everyone else..." If he's fumbling around with skill numbers and rolls and stuff you can and should encourage him/put a time limit on him.

Share the Spotlight

Also explicitly say to him "Please be respectful of spotlight time with the other players..." Just make sure they understand they need to keep their minion in a secondary role. Open and honest communication is the key, since it sounds like there's a lot of grousing either behind people's backs or in a passive-aggressive way in game, that's where you need to start. Maybe if he says he doesn't know when it's happening, arrange a signal you can give him when you think everyone's getting sick of the "guy and his minion show." Or encourage him to have his minion interact with the other players, to give them spotlight instead of taking it.

You should also be pressing spotlight-sharing as a GM - with a minion or not, some people are pushy; even out of combat you should be going around and making sure everyone gets an opportunity to participate, and don't hesitate to enforce "you're not there" in-game or even "let's hear what Joe has to say now" out of character.

I run a pirate-themed game where the PCs are the command crew and they often take pirate NPCs along with them on "shore runs." I ask them to understand their pirate's stats and keep them close at hand, and we try not to let them bog down the game. Some of them are "top tier" NPCs (one PC married one of them!) and we try to give them enough speaking time that they have detailed and realistic personalities, but PCs are the ones that get the opportunities to shine. That's just informal, organic collaboration between the GM and players.

Rules Changes?

Doing things like not letting them roll or other rules mods is usually a bad idea. They are a person with the party, and they should get Perception checks etc. like anyone else. However, there's a couple common speed-ups that are relatively minor in impact that you could consider:

1. You and all your minions going on your initiative count
2. Minion using Assist Another on your rolls instead of rolling themselves

Now, these can be nerfs... If they deliberately jacked up the Init modifier of their eidolon they're not going to want to hear "go on your init," for example - but they also save time. See if they affect the dynamic largely before you use them. Really, if the player is being efficient, rolling 2d20 and declaring "I see it but Jimbo doesn't" doesn't take measurably more time if there's not something else going on (extensive fretting over/searching character sheets...). With our pirates, for example, we have them go on the controlling PC's initiative but have separate independent rolls. (Having one color d20 for you and one color d20 for the minion and rolling at once helps - pretty much all basic time management tricks help more the more entities are in play).

Things like "your eidolon can't speak" or "can't make skill checks" or "has to be obvious" are cheesy crutches for a basic inability to actually talk about and work through the issues in Efficient Handling above. Don't do that. Talk honestly about the problem with the group and just get everyone to help with making the game flow better.

The Multi-Weapon Fighting Feat, has the answers you need.

Prerequisites: Dex 13, three or more hands.

Benefit: Penalties for fighting with multiple weapons are reduced by –2 with the primary hand and by –6 with off hands.

Normal: A creature without this feat takes a –6 penalty on attacks made with its primary hand and a –10 penalty on attacks made with all of its off hands. (It has one primary hand, and all the others are off hands.) See Two-Weapon Fighting.

Special: This feat replaces the Two-Weapon Fighting feat for creatures with more than two arms.

The 'normal' entry is the only place in the SRD that I can find where fighting with more than two hands and more than two weapons is covered. The Two-Weapon Fighting entry in the Combat section is short and refers only to wielding two weapons at once.

Extra attacks from BAB are not the same as extra attacks that you get from wielding a second (or third) weapon. Those apply even if you are multi-wielding (ergo, a 7th level fighter with 4 arms wielding four shortswords with the Multi-Weapon Fighting feat would have 5 attacks - 4 from multi-wielding, calculated using a base attack bonus of 7, and then another from high-BAB, on his primary hand, calculated using a base attack bonus of 2 (7 - 5)).

Notably, the eidolon's limitation on natural attacks by RAW does not apply to manufactured weapons, and natural weapons can be used as 'secondary natural attacks' (-5 to hit, 1/2 str bonus to damage) even if your main attack routine is with a manufactured weapon.