Michelle Wills Hart answered my distress call, writing to tell me she had a black faceted Dollar Pencil with that same clip which was available. When it arrived, I took a close look:
Yep. It’s a different variant. I’ll have to wait for the next one to come along for a donor, and in the meantime I transplanted a clip from another donor that turned up to complete my black clipless wonder. That makes four variations of the black Eversharp dollar pencils with Equipoised mechanisms:
Round, faceted (one piece), faceted (with fused round nose) and faceted with a fused round nose and a yellow accent band.