I've done something similar for a monster in my game using anglelerp. Hopefully I can word this so it makes sense.
I'd set the first segment's angle like this: anglelerp(MouseTail0.angle, Mouse.Angle, 0.2)
Then each following segment would be lerped to the previous one's angle . For a more natural flow you may want to decrease that last value a little bit with each one. So the first might be 0.2 as above and then 0.18, 0.16, 0.14 etc.