Jaws does have an auto advance facility. To find it:
First, look in Jaws Help to see if there's already something configured for your display. If there isn't:
1. Start the Jaws keyboard manager.
2. If your Braille display doesn't say "Default" (without the quotes) type "default" relatively fast. Probably just de will be enough.
4. Type BrailleAutoAdvance.
With luck the next word(s) will be the key(s) to start and stop the auto advance mode. Without luck it'll say None.
5. If it says None press the down arrow a time or three and see if there's anything that looks like it might be relevant.
6. When you find the script you want and you don't like what it's fastened to, press Delete on the keys you don't want and then Ctrl+A to add the keys you want.
"Never imagine yourself not to be otherwise than what it might appear to others that what you were or might have been was not otherwise than what you had been would have appeared to them to be otherwise."