Shader to change color of the part a object inside another object?

I’m working on a project and I have a task to move a player controlled sphere inside another sphere (fixed in space) and I’d like to make it easier to know when the player controlled sphere is inside the other spheres, or show how much of it is inside.

I thought that the way to go might be to change the shader of the player object when it’s inside another object (or the part that is inside), and only come up with changing color when behind walls.
Basically I want to change the part of the game object that is inside another game object into a different color.

Something like this:
78587-capture.png

In this case the player controlled sphere is the small one and the fixed “target” sphere is the bigger one!
(I made this with a simple shader that displays the object in different color when behind a “wall”, so to speak)

Is this maybe a culling problem or just a matter of changing shaders to a custom one? (sorry if I’m asking the completely wrong questions, I’m new to Unity)

I hope I explained the problem well enough. I tried writing my own shader but I’m a beginner in Unity so Shaders are kinda scary, even after watching a few videos.

Hi you might want to take a look at a custom shader.

Here’s an example.
Silhouette