The general rule of thumb (this varries for some species), but it does apply to Eclectus is this....
When looking at the beak closed from the side the tip should not extend past the bottom of the lower beak where it meets the jaw....
That being said, for beak work I strongly recomend a quality vet. I do beak work, and it has taken years to learn the structure and what is too long or mis shaped for what species. There is a lot more to trimming beaks then just cutting the tip off, and if done wrong it can cause the beak to grow incorrectly. The best advice is lots of different toys so a bird can keep the beak in top shape naturally.