Don't use TimeMachine or any other backup software to make backup copies of your database files while they are open. The copies, at best will trigger a consistency check when first opened in FileMaker and at worst could be corrupted copies. Use FileMaker or Filemaker server to make a local backup copy and then have your back up software make backup copies of this closed copy of the file.
If you are using FileMaker Pro to host the database, you can use Save A Copy as... from the host computer to save a copy of the file for use in back up purposes and this can save a copy to a drop box folder. And this can be scripted. If you host from Filemaker Server, you can set up a backup schedule to do the same.
Thank you for your reply. This is an excellent suggestion.
Sorry, obviously I meant to mark PhilModJunk's reply as the best answer. Thanks again.
Sorry, long day. I meant to mark PhilModJunk's answer as the best. Thanks again for your time. D