Rather than trying to quote and answer multiple posts, I will just say that the spell specifies One Object. Period. If that one object gets split into parts, then only one of those parts continues to glow as the source of the light spell. So one piece of the stick still glows, one piece of that pie still glows, one single marble glows. But only one marble glows to begin with because each marble is a different object. This is the definition of one, singular, only. This is not a DM ruling.
As for a larger object, the spell gives you a max size of 10 feet in any dimension, so a 10x10x10 cube could be used as the source for the spell, but a 50 foot length of rope would not because the length exceeds the max size, whether coiled up or not. The first 10 feet would not glow, the spell would fail.
Also, in my DM view, the spell still has a center point for the light radius, whether you are casting it on a penny or on a 10 foot boulder. So to me, it does not matter where on the object you touch it to cast the spell, the center point of the object is where the light emanates from. And if that one object gets split into parts, whichever part has that center point is the piece that still glows. The only way I would let this disrupt the spell is if you somehow split the item into precisely two halves, as that split would go through that center point, making that point no longer exist. In my DM opinion also, the center point of the spell would automatically shift to the new center point of the remaining piece of the object that it still glows from.