So I’m running an insurgency mission and start the mission out with BLUFOR commander only spawning units and owning mil objectives at the start. I’ve set civ objectives to objectives only, so that the insurgent force can establish themselves early on.

However, the BLUFOR commander only captures about 1-3 civ objectives before staying idle and not sending units to capture anything.

I’ve set the commander up on occupation mode so I’m not sure if it would work better on invasion, but do the civ objectives need to be attacked first and then they send troops or should they go and capture every vacant civ objective on the map?

Objectives should be fair game so long as the module is synced to the commander. Setting BLUFOR to invasion will reduce the number of groups used to hold territory, freeing some up to take more ground. If that still isn't enough, or if you prefer the stronger defensive strength of occupation, the commander will probably need more troops at its disposal.

I’m currently experimenting now, what I’ve worked out in the past is that if you have too many troops the AI Commander won’t do anything at all and only the smaller force will attack, regardless of commander type.

Are you sure? I experienced a lack of aggression if one side had too few units to actually use any to attack. Therefore I removed tiny and small military placements by filter because that way the OPCOM wont waste resources on trivial positions.

What is the number in max simultaneous attacks on your mission, how many objectives for each commander and the number of profiles?

all influence on the OPCOM decision

Started with 5 max simultaneous, which I bumped up to 10. About 120-140 objectives and around the same amount in profiles.

That will almost certainly be the issue. Invasion commanders will aim to use 2 groups/profiles to defend each objective. I don't know 100% if all objectives "behind the lines" will do this, but it seems so. So that would be ~250 groups if that 120-140 is for a single commander. Occupation is 5/objective I believe so even more troops just to hold them what they already have.

Try adjusting # of objectives down and profiles up to get closer to where you want to be.

What about max simulataneous attacks? What would you recommend for an occupation commander which only owns mil objectives at the beginning?

What's best for that setting will depend on how many and how distant objectives are in you're particular mission, how many troops commanders have, and how fluid you want the situation. The more objectives there are the more this setting is dampened at a particular value, and higher value will produce a more volatile battlefield than a lower value. Eg. having it at 10, with 20 objectives each means a commander could lose half their territory in one series of attacks, whereas with 100 objectives each, it would be 10% at risk. Having it at 2 will be a more static scenario in both cases, all the more so with 100 objectives.

"Easiest" would be try at default with the force size/objective load you want, then see how it plays out and how you might want to see it change. Greater or lesser force density, slower/faster progression by a particular side, etc. Multiple dials that all work together, one or more of which may bring about a desired result through different means. :)