Is there a type of mosaic Down syndrome that doesn't require the mutation to come from either parent to have a downs child?

Yes. A mosaic down syndrome child can come from a normal egg and normal sperm, produced by normal parents. The fertilized egg would start out normal with 46 chromosomes. It can divide into 2 normal cells, which themselves divide again. If on one of the early divisions, one cell ends up with an extra #21 chromosome and survives to continue dividing, the child will be mosaic with some trisomy 21 cells.
See below. You may be talking about a spontaneous mutation. Neither parent has downs. But a mutation in the egg cell or sperm cell produces the child with down's.