I have searched and searched parish records for the Etheringtons prior to Cawood. There is no baptism for a Thomas that matches anywhere in Yorkshire. I thought maybe Thomas was the father of Thomas Etherington a quaker watchmaker from York, whose family originated in Fulford (the parish where Thomas of Cawood's wife came from), but Thomas Snr's son Thomas appears to have died around 1730. So I am stuck.
The closest family groups of Etheringtons are at Riccall (names William & Richard) and at Heslington (George). There are some wills for Heslington (which adjoins Fulford) at the Borthwick that I have not yet checked.