One of Thomas's half brothers, son of Cath Christian, was Robert BANNAN bapt 25 April 1813 Andreas.

I guessed that Robert was the father in this marriage, but again no baptism found for his son Robert:
Marriage 21 July 1860: Robert Bannon laborer Andreas, father Robert Bannon, shoemaker & Ann Radcliffe Andreas, father John Radcliffe farmer.
Witnessed by John James Radcliffe. [Witness was Ann Jane’s eldest brother.]

Ann Jane BANNAN, aged 67 buried German 25 Mar 1910.

1881 census: Dwelling 10 The Green German – Peel:
Robert BANNON Head M Male 41 Andreas Agr Lab
Ann BANNON Wife M Female 41 Andreas Char-Woman
Robert C. BANNON Son Male 12 Andreas, Scholar
John C. BANNON Son Male 10 Andreas Scholar
Margaret E. BANNON Daur Female 8 Andreas Scholar
Willie A. BANNON Son Male 7 Andreas,Scholar
Ethell C. BANNON Daur Female 5 Andreas, Scholar
James BANNON Son Male 3 Peel,
Henrietta BANNON Daur Female 1 Peel.

There were bapts in Andreas and Peel for their children, above, but the earlier ones could have been Roman Catholic?
Brian Lawson has listed dissenters' births on his website, but not pre-1817. These include:
8 Apr 1846 BANNON, John son of Charles BANNON & Anne BYRNE R 88.

Sue