your images show an opaque green + yellow bead that might be made of fused (not completely melted) powder glass resembling Krobo beads from Ghana, but it is also very similar to a bead type that used to be described as a Roman period "Date bead" - with a fairly wide hole- roughly oval or bulbous shaped,- green with yellow at one end... around 1 cm long... sometimes striped as shown from my collection. -maybe there is a more up-to-date description?

Very helpful, thank you. I’ll keep my eyes peeled for similar beads when looking at krobos and fused glass. Does the yellow “patch” material on your beads you pictured have a wood grain or marbling pattern? Though I didn’t manage to photograph it, the end “patch” on the bead I have has such a pattern.

Searching for Roman and date beads brought me to this strand. These look identical to my broken bead. I don’t often trust the identification of auction sites but it says they’re Roman. Does that seem right?

yes these green and yellow get described as Roman date beads - i don't yet have more exact information... but clearly it seems to me that the necklace you linked to, has been put together by a "designer" using other beads added to create the pattern. so it can't be assumed that this necklace is an authentic roman necklace, but recognisable roman beads are featured in it.
There are "gold-in-glass" spherical beads -which were known to have been made in that era, and then small dark and light faience ring-shaped beads such as were made and used generously in new kingdom Egyptian necklaces in burials ... giving a striped appearance between the featured beads. maybe they were all found together??

Robert Liu describes them as "Ptolemaic or Roman period glass beads from Egypt...Solid colors capped by yellow are called date beads." (Page 125, Collectible Beads: A Universal Aesthetic)