Hi there
I've made shadows from normal maps without using of height map data, don't remember anything like this and failed to google such thing, so decided to write an article and made demo application of this effect.
Benefits i see are: no extra video memory usage; no need to create new textures (for the forward render unsure, cause same problems as with parallax exists).
https://i.imgur.com/UkK41ih.jpg
Anyway, link to Normal Mapping Shadows PDF and it's demo is http://enbdev.com/doc_normalmappingshadows.htm
Hope this helps with your work. Stay safe.