Nothing came up on FreeReg. Ancestry has a tree:
http://trees.ancestry.co.uk/tree/720074/family?cfpid=-2035941103 with a Thomas Wyatt from Topsham. Can't tell where all the info comes from.
FMP has the image of the marriage you mention - no father's name. Both bride and groom made their mark. Banns. Witnesses were John Milden X, Thomas Williams. Looks like Thomas Williams was the Churchwarden - he witnessed all the marriages on the page.
There was another Thomas Wyatt marriage on 2 Jan 1781 at Ermington. Bride ~ Ann Pearse X. Witnesses: Elizabeth Grinslade X and, guess who, Thomas Williams. Licence. Looks like this Thomas Wyatt signed his name, seems the only difference between them. Again, no father's name.
No burial for an Ann Wyatt listed between the two marriage entries.
Sorry, can't help more than that.