In reality, unless a mutation results in a gene not being transcribed/translated (ie. "silenced"), they are expressed even when an individual is split to a recessive mutation. It's just that we don't see an effect with our eyes that differs from an individual homozygous for the "normal" version of the gene. But that's a limitation of our eyes -- if you measured things differently, there is an effect. For example, let's say you have two black cats. One is black split for the Siamese/ColorPoint mutation, the other is homozygous (or "pure") black. Just looking at them with our eyes, we can't tell them apart. HOWEVER, if you were to measure the actual amount of melanin deposited in the hairs, there would be a difference. The "pure" black cat will have more pigment in its hairs than the black split to siamese cat. It's not enough of a difference to be noticeable with our eyes, but it is enough of a difference to be able to be measured in a lab.
So, we classify a mutation as recessive when being heterozygous for it shows no apparent difference. But within the body, there is a difference -- individuals with two copies of the "normal" version of the gene will produce more of that protein than individuals with only one "normal" copy. When the mutation is considered recessive, the less-than-"normal" amount of that protein is still enough to give the "normal" appearance. The mutated protein doesn't work the same way, but at the same time, it doesn't interfere with the "normal" version working the "normal" way. Only when there's no "normal" version of that gene present (i.e. the bird is homozygous for the recessive mutation) do we notice the difference -- because there's no "normal" version of that protein being produced which is required for "normal" appearance.
Now look at co-dominance, incomplete-dominance, etc. This time, the mutated version "does something" that either interferes with the "normal" version, or blends with the "normal" version to give a "blended" phenotype. Co-dominance is classically illustrated when there's a gene with one allele for red petals, and one allele for white petals, in a particular flowering plant (I think it was petunias, but I'd have to go back and check). Have two copies of "red"? The flowers are red. Have two copies of "white"? The flowers are white. Have one of each? The flowers are pink -- not red splashed with white, but an even pink. In this case, it's as though the White gene reduces the overall amount of pigment produced evenly. "Pink" flowers are thus "red" flowers with an even decrease in amount of pigment. But in appearance, we interpret it as both genes being visible at the same time, resulting in a blended phenotype that is neither one nor the other.
Incomplete- or partial-dominance is slightly different, but again, it's based on how we interpret the appearance of the phenotype. An example in peafowl would be any of the white-spotting mutations (White, Pied, and White Eyed). Have no copies of either? The pea has "normal" pigmentation. Have one copy of either? The pea has some "disruption" of pigment, but not as much as having two copies of either. Why the spotting rather than an even dilution? Possibly because the white-spotting genes affect pigments produced on-site to not "fit" into the feather tubes, leaving filaments without pigment. Since pigment is produced for feathers basically right where they'd get deposited (as opposed to somewhere like the liver, and then floating through the bloodstream to be evenly dispersed), if one cluster of melanocytes (pigment-producing cells) makes the "too big to fit in the feathers" pigments, that cluster will result in a section of unpigmented feather (not necessarily an entire feather). So one copy of the gene will make the faulty pigment, but the "normal" copy will make the "normal" pigment that CAN fit into the feather to be deposited.
In peas, look at the White Eye gene, which we call Incompletely- or Partially-Dominant. Why? Because when there's one copy of White Eye, we see an effect. Why is it not Co-Dominant? Because we don't see a blended phenotype -- we see a patchwork phenotype -- in birds which have only one copy of White Eye. Some ocelli are white, some are "normal". We don't see "gray" ocelli all over -- we see some of each. When a pea has two copies of White Eye, then all (or virtually all) ocelli are affected.
OK, then what goes on with recessive mutations that "dilute" pigment? Well, it's hard to be specific since I haven't studied them specifically, but I can say that there is no one gene for melanin. The pigment is produced through a series of reactions, involving proteins that are either directly synthesized from genes or are the result of other reactions. Let's think of making melanin like making a cake, and the separate ingredients and tools are the proteins involved in its production. Some come from genes (things like, for example, eggs...or milk..or other ingredients that are "harvested" as-is) while other ingredients come from previous processes (things like white flour, which had to be refined from wheat seeds). Then you have the tools -- mixing bowl, egg beater, etc.
If you delete one of the necessary tools, like a mixing bowl or baking pan, you can't make the cake at all, and you end up with no cake (like an albino, which has no melanin). If you change an ingredient, you'll get cake, but perhaps not the same cake. Let's say you use whole-wheat flour instead. You'll have cake, but it won't be as fluffy -- it'll be a little more "bran-y". Or perhaps you switch out the four chicken eggs in the recipe for four goose eggs. Goose eggs are larger, so you'll have an "eggier" cake. With mutations that modify (but don't delete) the pigment, you're changing one of the ingredients, resulting in a modified cake. Perhaps the cake won't rise as much, so it'll be smaller in volume. Perhaps the mutation "reduces" sugar -- having one copy results in 3/4 of the "normal" amount of sugar, and having two copies results in 1/2 of the "normal" amount of sugar. You can still get a cake that's "sweet" with 3/4 the sugar, and you probably won't notice it much. But delete half, and there's a noticeable difference. That's like a recessive mutation.
The white-spotting mutations clearly don't result in the peafowl being unable to make pigment -- they have pigment in their eyes -- just that the pigment doesn't "fit" into the feathers. That's like making a cake in a pan too large to fit in your friend's fridge -- you made cake, for sure, but you can't put it where you thought it should go (It might be the other way around -- the white-spotting genes might make the feather tubes too small to allow the pigment to get through, which would be like your friend not leaving you enough room in the fridge for your cake -- I don't know, but you get the point).
ETA -- one often hears that a white mutation "isn't albino" and it seems odd that someone would just insert that. What's the difference? Well, albinos can't make melanin, whereas white non-albino animals CAN make melanin, but it just can't "fit" where it "normally" goes. So? Well, making melanin involves steps that are important for making other VERY IMPORTANT substances needed for other things, like certain neurotransmitters. If the "mistake" that prevents melanin ALSO prevents (or severely interferes with) production of those neurotransmitters, then you have the "unhealthy" effects sometimes seen in albinos. But that's a whole other topic....
At the DNA level, unless a mutation results in a "silenced" gene, there's not much difference between a recessive, co-dominant or incompletely-dominant mutation. We assign those labels based on what effects we see in the individuals. The genes aren't "battling for dominance." If there's any dominance, it simply means that we can see an effect when there is only one copy of that version of the gene. Recessive simply means the effect is "hidden" from our vision, even if we can detect an effect using other tools (such as with the cat example I mentioned in the beginning). For example, if someone had the blood type of A+, but his mother was O- (meaning no A and no Rh proteins) you'll know that he's split for O and for Rh-, even though he "types" at A+. But if you were to measure the actual amount of the A and Rh proteins produced, it would be less than that produced by a person "pure" for A+. When we blood type someone, we just check for presence -- not quantities -- of specific blood proteins. If you have the A and Rh proteins, you are A+.
