Thank you very much for you fast reply !!!
Indeed I’m really confused by the concept of Function, Float and Vector
I come from the 3dsMax / Vray world and there, when you create textures and materials, everything can be mixed together
A noise texture, for example, is considered as an RGB texture (as far as I know)
It’s really hard for me to understand the concept … I’m sure it is related to the way graphic cards deals with shading
In my case, I use a mix of procedural textures to animate a rain drops texture :
When I plug the result in any slot (Base Color, Emissive etc.) everything works as if it was an texture map … (it is really frustrating cause I only want to use it as a normal map) 
My setup is really complex and I wish I can avoid multiply it by 3 just to be able to create a normal map
If only I could offset the texture just before pluging it into the NormalFromFunction box … here it seems I have to duplicate my whole graph 3 times
I thought I was close to the goal when I saw my animated black and white texture
I will try to replicate what you post on your screenshot and see what appens
Once again, thank you for your answer