Logbook Question From An Outsider

Greetings,

Would somebody be kind enough to answer a question from this first-time
poster?

Over the years, I've accumulated several dozen hours in Frasca and AST
300 simulators...of course, legally classified as ground trainers. I
have been under the impression that time in these ground trainers does
not count towards my total time. This is borne out by my computerized
logbook which qualifies any time in a "ground trainer" with an asterisk
and does not add it to total flight time.

However, I recently spent time in an AST300 with a very experienced
instructor who said that it does count towards total time, although I
cannot log landings or P.I.C.

What is the correct way to log time in an AST300 or Frasca?

Thanks very much.

-Jim Gorman