I think it's a lot of guess work, but I do have a theory as to why the council of 13 probably did exist before the andalites came along.
Firstly, I think the #13 is completely arbitrary. I think K.A. Applegate choose it, because it is an unlucky number in America. You can find rational to make it fit from there, such as there being 13 major pools on the yeerk home world. I wouldn't tend to think that was the case, though. Besides a few debatable occasions, most advancements in early human history didn't happen in multiple places simultaneously. Typically, an idea is developed in one area and then spreads to other places, because people do what makes their life better and they'd try it out as the idea travels. I just can't see 13 yeerks randomly figuring out that they can climb into the heads of 13 gedd at the same time. I would think it was much more likely that one pool had one yeerk figure it out and then let the others know. Then they ended up traveling and discovering the other yeerk pools and exploring them, thus spreading the idea and causing other yeerks to attempt to capture hosts.
Basically, like one other posted stated, I think you could safely categorize a government as any group that takes charge of their people, have the means to enforce their orders, and are recognized to have authority. 13 yeerk hosts don't seem like a lot, but when you're the first governing group of your kind, it doesn't really matter how small time you are, because you're still the biggest governing body to ever exist on your planet. You can stop and think about what the actual word government means. Just looking at it, to me, it means someone who governs others. This could mean one person leading a small group of people, or a massive group governing a nation. It's just one of those words we hear and don't think about because our brain automatically snaps to what we "know" it means. It's like when you talk about your bike. Some peoples minds snap to bicycle and others snap to motor cycle.
In this instance, the reason the yeerks would need a government or council is because inhabiting the gedds give them power. Those in power, as the yeerks show throughout the series, want more power. They know there aren't enough bodies to go around. Being honest, human beings would be the same way. If there is a limited resource, be it entertainment, oil, or anything else. Most humans aren't content to take a turn and say, "Okay, I'll sit back until everyone else has had a turn." Even the honest people who might feel that way will get upset when someone else cheats and they'll be done with the concept.
The yeerks would be the same. With a limited number of bodies to control, they'd want to make sure they had access whenever they wanted it. They'd dole out extra access to their friends and others with whom they'd use it as a means of control. I could definitely see the council of 13 being made up of 13 different home world pool's representatives somewhere down the line. After the idea had spread around. The original pool probably wouldn't be able to control access to all the gedd, even if they'd had the foresight to do so. Still, it seems unlikely that once a power struggle began, that one or two pools wouldn't end up controlling all of the resources.
Additionally, there is the issue of them having to come back and bathe in the yeerk pool. It's been a while since I read the series, and someone can feel free to correct me, but I believe that they had to bathe in the yeerk pook regularly, even on the yeerk world, because they couldn't get the rays from their sun that they needed to survive when they were inside the hosts head. I think the difference between there and earth was that they had a special light set up above the pool on earth and any pool would be exposed to the suns rays on the yeerk world, but they still have to soak them up to live. This would cause them to be vulnerable. The gedd could run away, another yeerk could climb into the hosts, etc...
I feel like that was another driving force behind the need for a group. Each yeerk would need one or two allies to make sure their host remained and no other yeerk tried to use it. The initial group was probably the same as the current group of 13. They weren't friends but had a mutual interest in protecting each other's hosts and maintaining their groups power. They'd sr**w each other over if possible, but they'd be worried that betrayal might not be successful, leading to repercussion for them, or might lead to betrayal of them in the future, so there was a grudging alliance.
That pattern just continued into the present, adjusting for expanded control of the larger group. The reasons I mentioned above don't clash with any of the actions I remember the council or other yeerks displaying. Better hosts and assignments are doled out to yeerks that prove themselves. Some yeerks are even denied hosts when they fail. Access to the yeerk pools is another means that the governing body uses to control the subordinates.