@RRK, as far as I know, I am aware of superimposed ignitors for the low wattage low voltage North American high pressure sodium lamps. Examples include the Payne Sparkman ULI-050S ignitor and a few other ignitors I have mostly seen being sold in some South American countries.
See here:
https://www.lighting-gallery.net/gallery/displayimage.php?album=search&cat=0&pos=0&pid=237036
I said "not practical", not "not possible"

Low voltage HPS have short arc lengths and until not deliberately made with high xenon pressure, require low ignition voltage with low energy. Easily satisfied just with a tapped ballast choke. Not much need to wind an extra transformer. And there is not much reason to remote ballast such a low wattage lamp....