No, homunculi cannot help. But it depends.
Unlike a familiar, a homunculus does not have skill ranks equal to their master's skill ranks. That phrase, "A homunculus knows what its master knows and can convey to him or her everything it sees and hears" is not talking about skills known, or spells known, or rituals known, but talking about how connected telepathically they are, constantly sending information of what one sees and hears to the other, so you dont need to metagame that information, their link sends information to both sides of their telepathic link.
To cast ritual spells, you must know some (or all) of the skills associated with the ritual. For Wrest Resources, that means Knowledge (geography), Knowledge (nature) or Survival. While casting a ritual without secondary caster will require you to know all skills associated with it, as you will be making all those checks yourself, the aid of secondary casters allows you to reassign some of those skill checks to the ritual's secondary casters.
So, unless the ritual requires one of the skills that your homunculus actually knows, either those base skills (Fly +10, Perception +3, Stealth +12) or another skill taught to them by other means (ie: Borrow Skill), for the purpose of making those skill checks, they cannot help either as primary or secondary casters if they don't know those skills, as you cannot make untrained Knowledge checks with a DC higher than 10.
And if you use the rules for creating and modifying constructs, it should then be possible, as you can grant them extra HD and skill ranks. But they will get expensive really fast, making it a much better option to create magic items that grant you (or whoever wears the item) bonuses to those skill checks.
Regardless of the method chosen, animated objects with a Brain mod should be cheaper than any other construct type for the purpose of hitting those high DCs.
But other creatures could, if they know the necessary skills
However, as I said, any creature that has any of the require skills may help in the ritual as secondary casters. Only the primary caster must know the ritual, because they are who discovered the occult ritual.
To cast an occult ritual, the primary caster must learn the ritual’s secrets (see Discovering Occult Rituals). Secondary casters can assist in the casting without fully understanding the intricacies of the ritual.
Since most unintelligent undeads or constructs won't have the necessary skills to be able to aid you (and even some intelligent ones, like ghouls), you will notice that more powerful undead, like vampires, have several ranks in knowledge skills and could help in making those checks.
Your best bet is probably to create intelligent undead that apply a template to a creature that had the necessary knowledge, such as enemy spellcasters or sages. A skeletal champion will retain their knowledge and gain a couple more skill ranks based in their racial HD (if any).
As for summons, even if you summon a very powerful outsider, they likely won't be strong enough to meet the required skill ranks, as they are much weaker than the spell that summons them. You could have much better luck using Planar Ally/Binding spells, though.
However, if all you want is the bonus for every 4 secondary casters (up to 20), you could hire a few commoners for a few silver coins and get that +5 bonus. But I assume that this was never a problem for you. And yes, any creature here helps, it doesn't require any skill ranks or special knowledge, and the rules don't mention they have to be intelligent either, so mindless undead should be as valid as constructs and living creatures.
But the best advice I can give you is to learn and use the Visualization of the Mind spell before casting occult rituals, and make all those missing skill checks yourself. Especially for a ritual that requires such high DCs as the one you want to cast.
Duration 24 hours or until discharged
You enhance a single aspect of your mind, nurturing and empowering it. Choose a single mental ability score (Charisma, Intelligence, or Wisdom). You gain a +5 bonus on ability checks and skill checks associated with that ability score.
Intelligence: You immediately gain a flash of insight, and gain a number of ranks equal to your Hit Dice in any skill in which you have no ranks. These ranks last for 1 minute, during which time you can also treat that skill as a class skill.
Creating a few Scarlet and Blue Sphere Ioun Stones (4,000 gp each) for this purpose also helps, as it will grant you one skill rank in the associated skill per level (similar to the Headband of Vast Intelligence), which should be enough to fulfill the ritual. And yes, this may also be given to your homunculus so they gain the necessary skill ranks to make the ritual skill checks.