In order to make a particle system trail data, select the type data and set it to New AnimTrail Data.

You will need to set the trail as an Anim Notify in the animation track of any animation you want it to appear in. The trail texture that you use should be set-up similar to many VFX textures of this type, wherein it is clamped and not tiling. See below:

Set the blend type to Additive and enable two-sided material as a property so that it shows no matter what camera angle is used. In the particle editor, remove initial velocity to prevent noise appearing.