The Authority is there to enforce regulation. There is no regulation regarding simulator time because it is not flight experience. The one exception is where you are using a simulator as part of an approved course and it is credited in lieu of flight experience. If its your job as a TRI then its a good idea to keep a record, how you do that is up to you. Apart from proving to an employer what you have done of for providing a record of hours for revalidation purposes, the time is of no use for anything else. I always put sim time in the back of my log book.