I would guess that you can just create a function to detect when the ship has stopped moving forward and then turn off the emitter. As for the trail going away from the ship opposite another emitter on an empty game object is probably a good starting point.
After a few trials and errors I managed to get things almost alright. I changed shape of emitter to be box, moved it to center of my ship, set initial speed to 0 and set inherit velocity to 0 and emission to distance instead of the time.
Now I probably need to make infinite particles and destroy them when they hit invisible planes behind and front of my ship.
Well after relooking Elite I decided that spaceships move forward only - makes life easier.
Final solution I did was to create emitter as a box make it wide enough that particles goes far enough to look nice (gives feeling that you’re moving, pitching or rolling).
Speed I set to very slow and now it looks like slowly moving “stars” that accelerate when ship accels. Adding nice skybox will give final touch for now.