Backup lights are backup lights. I’ve had a headlamp fail while descending in the dark after a long alpine climb. Whipped out the backup (1x18650) with a lanyard around the wrist and was good to go.
I have one of those headbands. I guess they’re ok for backup purposes, but pretty darn annoying otherwise. Even a Convoy S2 is a little too heavy for it and it wiggles and bounces around as you move your head. Probably better for a small 1xAA light. For 1x18650 lights I prefer the lanyard around my wrist.
My own recommendation for a caving backup light is a zoomie. Nice for the close up stuff such as rigging and passing anchors, and with the option of narrowing the beam for longer viewing. This one is liked by many: Review: Zeusray CREE XM-L2 zoomable flashlight
I don’t have one myself as a prefer a wider beam for other uses, but might get one as a caving/mine exploration backup as this one is a little smaller than the ones I normally use.