Texture painting giving me a hard time

Hello, this is my first time posting here and I wouldn’t trouble you guys but there doesn’t seem to be a straight, working answer to my problem.

My first serious Blender project is that problem: I’m trying to paint directly on the 3D shape (since I usually fail at 2D work) using one material and two principal textures, of which one is the base and the second is supposed to be mostly transparent, containing fine details such as lines and small imperfections.
More are to come for noise, different gloss and such, but I need to solve this first: the second texture absolutely refuses to function properly.

While working in Texture Paint the texture (which is a still completely empty PNG with alpha channel in place) shows up white in Solid view, and black (with highlights) in Rendered view.

I’ve made sure all the settings are correct as per all instructions I could find including on this forum, but nothing works (for example, I made sure the Alpha is present but at zero by making the PNG file through Blender itself, then ensured the texture uses Alpha and influences it fully - the slider is at 1 - and also that the material has Z transparency, with Alpha and Specular at 0. There were other adjustments as well).

No matter what I do, with one exception that defeats the purpose of the texture (ticking RGB to Intensity), it shows white in Solid mode and black when rendered, unless I put the base layer, which works properly, on top.


In solid mode it looks like this:
In rendered mode it looks like this:
This is the top of the project, so it looks far from the black I claimed due to lighting.

When it should look like this (and does if I hide the bad texture under the working one):

And it should look something like that in solid mode too.

PS: the white in Texture Paint baffles me especially. What’s the point of it, even? Why not just let transparent be transparent, and let underlying textures, if any, show through as they should?