So, I just unlocked another half level of finding names going back by
finding my great-grandfather's death certificate which had his
father's name on it - Jonas Steinberger. This sort of jives with an
older reference I had (non-official) that his name was Yonah.

I know my great-grandfather was born in 1877, to give a point of
reference. Unfortunately, I don't really know much more about this
branch of the tree. Thus, I've been trying to find any records and
connections going back up this line.

However, I'm unsure of where I can go to search any records of
Austria-Hungary to try to learn more. I'm used to searching Polish
records and using JRI-Poland, but the relevant link on the SIGs page
doesn't seem to have that functionality.