By the way Peter, you are correct that the acid need not be heated
but, hot acid 'encourages' the carbonization to a greater depth
and it seems to work a bit faster. Kind of like cold pickle will
also do the job but hot pickle works faster.
The recipe I saw involved soaking the stone in the sugar solution for
literally months, and in the acid for a week or so at least.
Apparently, those guys weren’t worried about speed. This recipe was
old instructions I saw somewhere of how it used to be done in Idar
Oberstein, if I recall. Not sure, but it was an old traditional
method. I think it was in a small spiral bound book/booklet I bought
a couple decades or more ago about how to dye stones. It’s around
here somewhere, but I didn’t see it immediately on the shelf when I
looked, so I can’t easily go back and check. If I happen to find it,
I’ll follow up on the thread if you like.