Since I cannot see it in person and am not able to see any agate like indications in your photo, I find myself wondering whether you are you certain it isn't glass? -The white stripe and surface texture reminds me of glass.

Also, it reminds me of beads from Burma -the colors, size, shape and concept.

The word "dZi" is being wishfully applied to anything recalling dZi beads.

Just my thoughts,

Fred