Producing 50% chance like the mutant gene parent when bred to a normal is due to being the heterozygous genotype and not specific to the mutation type. For example:
1. Het albino X normal = 50% chance hets
2. Pastel X normal = 50% chance pastel (many don't call Pastels hets but genetically they are heterozygous for the pastel mutation)
3. Pinstripe (at least all except the one proven homozygous so far) X normal = 50% chance Pinstripe.
What determines the mutation type (recessive, co-dominant, or dominant) is how the heterozygous looks (phenotype) compared to normal and compared to the homozygous mutant. Example 1 is a recessive mutation type because the het albinos look normal and only the homozygous albinos are visible morph phenotypes. Example 2 is co-dominant because the heterozygous pastel genotypes are a visible mutation (the Pastel phenotype) and the homozygous pastel genotype are a different phenotype (Super Pastel). Example 3 is the dominant mutation type because the heterozygous and homozygous mutant genotypes are the same phenotype (Pinstripe).
There is not a public proven homozygous spider yet so we still don't know the spider mutation type. If a spider is eventually produced from spider X spider breeding that then goes on to produce a large number of only spiders bred to normal and that spider looks and acts like other spiders then we can assume that spider is dominant. However, given how long spider has been around without this happening it's also possible that spider is homozygous lethal and the eggs from a spider X spider breeding that would have two copies of the spider mutation don't hatch. This would be different than the heterozygous spiders so I think would technically qualify spider as a co-dominant mutation.