I have 3 possibilities, one of which is the one Frances suggests, but I don't think he's the right one.
I have this for the Thomas b 1811 s/o Paul & Elizabeth.:
"SLC Extract June 2014 1851 Episc #8 Braddan Thomas Gelling
Petition Robert Gelling of Douglas
About 31 Dec last Thomas Gelling brother of above, Master of the Schooner "Foxdale" left the Port of Liverpool bound for Port of Douglas. Heavy seas. Never seen again. No will found. Dated 10 Feb 1851.
Eccl Court Douglas 14 Feb 1851.
Appearing that Thomas Gelling some time ago departed this life, intestate and without issue, leaving the pet'r Robert Gelling, Paul Gelling, Wm Gelling and Diana Kelly wife of John Kelly now off this Isle his brothers and sisters and only next of kin. All decreed joint admin's."
I don't think he'll be the father of Ann Catherine because it's more likely she would have chosen Master Mariner as occupation of her father rather than Painter.
My other choices are based on the Painter occupation.
In the 1841 census at Knight St, Liverpool, there is a Thomas Gelling 30 Painter and Joseph Gelling 20 Draper, living in same residence at James Evans 45 Coach Builder and his family. All have "Yes" meaning born in Lancashire.
The Joseph above is a mystery. There is a Braddan burial record for "Mr Joseph Gelling" age 24 Aug 7 1844 which could be him. The "Mr" indicates he's likely from an important family..
One possibility for Thomas is the one born 5 Nov 1811, bapt 21 Feb 1812 St Peter Liverpool, son of Mathias Gelling and Mary Gaskell. This matches the "Yes" in the 1841, but there's no Joseph and Thomas was a butcher when he married Eliza Hull in 1850. Not a great choice.
A better possibility might be Thomas bapt 10 Apr 1812 St Matthews Douglas, s/o Thomas Gelling and Ann Moore. He married Ann Esther Bridson in Malew 1846 and they are in Liverpool in 1851 where he now is a Victualer. He's missing in 1861 (family is in Malew where she is a "widow"). He must have returned because a late child born in 1862. He's with them in Malew as an Annuitant in 1871. In the 1881 census he is a Painter again. He died 31 Oct 1883 age 71 of Ballasalla, buried in Braddan. Ann died in 1891.
Thomas b 1812 comes from a prominent family. His parents were both widowed when they married in 1808. Thomas Sr was baptized 29 Sep 1756 Jurby, son of Mr Paul Gelling (1727-1795) and Mrs Jane Gelling (1740-1826) of Ballavagher Braddan. Paul was part of the Gellings of Camlork. Thomas first married Mary Quark in 1779 Lonan, who died in late 1807 and they had 4 children born 1779-1785. The second family was born much later 1808-1814. Thomas Sr. died in 1835 and Ann in 1862. Her first husband was Thomas Thomas.
A drawback is not being able to find a Joseph in the immediate family. The 1841 doesn't provide relationships so Thomas and Joseph may be cousins or some other relationship. Joseph would fit nicely into the family of Rev'd Alexander Gelling of Arbory and Anne Clucas, which has a gap between 1817 and 1822. Alexander was the youngest brother.to Thomas Sr. Another possibility is Joseph could be a nephew, born to an older half-brother of Thomas..
Reading back through this, there's a lot of conjecture based on the Painter occupation and trying to fit Joseph from the 1841 census. I'll hunt around and see if there's more information somewhere.