Custom mesh trail in Unity

I also tweaked the cigarette smoke in a similar way but using my own shader for it. This option could work for me if the texture was tiled rather than stretched. Is it possible to tile a texture in your trail?

There is a problem with the Unity’s built-in trail.
When trail follows the character, the texture also moves very quickly along the trail. And it looks really bad. When the trail stops moving shader works correctly (like on attached gif). I am trying to find a solution to this problem but with no success yet.
Trail
Perhaps you have an idea how to solve it?