Do you have the marriage record of the daughter Eliza of Dunkirk and the death record of William's wife Mary Ann of Ostende? The marriage record could contain the place where her parents lived at that time and the occupation of her father.
I have just found the marriage entry at Dunkerque (Online Archives of the Archives
départementales du Nord) Dunkerque mariages 1830-1845, page 507 on the left side
Thanks for that, Svenja - very helpful. I did receive some information from one of Eliza's Belgian descendants a year or so ago and his research is confirmed by your findings. But he did find another record that indicated that Andre Thomas Fowler was the son of Eliza's sister Catherine, so it's still a bit of a mystery - he believes that Andre Thomas died just a few months later on 30 April 1831.
He also found what we think is the death record of Eliza's mother (25 March 1834 at Ostend), but her name is shown as Marianna Clarington of Kent (as you found) and her partner was stated as Henricus Fowler of the Marines, so it's not conclusive. However, there was a death notice for Mary Ann in the 8 April 1834 issue of the Kentish Weekly Post - it didn't state the place of death, but the date is close enough to Marianna Clarington's death to make it likely they're the same people (Mary Ann's maiden name was Claringbold, which is close enough to Clarington if we allow for language/handwriting errors). It's harder to explain the Henricus Fowler name, though, as her husband's name was William (when Mary Ann died, he was commander of the coast guard station at Dugurth, County Mayo, Ireland); I'm wondering whether William had a brother named Henry and it was he who was present at the death of Mary Ann. But I've not been able to find out anything about William's parents or siblings.
I've since found that William Fowler died on 24 January 1862 near West Cove, County Kerry, Ireland - he'd been the commander of the local coast guard station at West Cove since 1843. Two of his unmarried daughters, Jane and Charlotte, were living with him and were the only beneficiaries of his will.