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Using a Float4 - and converting it into a normal map - doable?

I’m currently iterating on a shader that would allow me to “paint” through vertex painting on a surface. What I need, basically, is for the alpha layer of a related heightlerp to be converted into a normal map.

I’ve tried a lot of ways to achieve this, but I always end up with the same problem: converting the alpha from the heightlerp into something usable with a normal map algorithm.

So far, this is my graph (and the error I get) when I try to do something that should, technically, work:

https://i.imgur.com/HtekoFY.jpg

Obviously the issue here is on the multiply node, since you can’t multiply a UV value. But how could I apply the UV coordinate, in this case, onto the float 4?

Maybe I’m doing it wrong. But I can’t seem to find a solution to this and it’s driving me nuts!