It's three years later but here's a possible connection for you Brian. You may already have these details.

As far as I know the names Quayle and Stowell first connected with Thomas Stowell marrying Deborah Quayle in 1762.

They had a son Quayle Stowell (christ. 1766) who died as an infant. Another child was also a Quayle Stowell (christ. 1775) who married Jane Oates in 1798.

That section of my Stowell tree comes to a dead end at that point.

Your Quayle may well be their son or one generation down.