re Tierbuck:
Sarah Tierbuck 27 Jul 1778 St. Martin, Birmingham, Warwick, Joseph and Sarah
Joseph Tierbuck 28 Dec 1779 Saint Martin, Birmingham,Warwick, Joseph and Sarah
Susanna Tirebuck 1 Oct 1781 St. Martin, Birmingham, Warwick, Joseph and Sarah
also:
Elizabeth Tirebuck 12 Sep 1785 St. Martin, Birmingham, Warwick, Joseph and Sarah
Matthew Turbuck 19 Oct 1790 Saint Martin, Birmingham,Warwick, Joseph and Sarah
I don't know if it's a coincidence, but there's a Joseph in London, marrying Grace Drew in 1806:
https://www.ancestry.co.uk/imageview...rce&pId=711336
Two of their three children (EDIT 4 children - one bap is in Westminster listings) show occ of father at their baptisms - gunmaker or similar.
Joseph died in 1815 aged 35, so b abt 1779/80:
https://www.ancestry.co.uk/imageview...71&pId=1622049
and his will gives his occ as gun maker:
https://www.ancestry.co.uk/imageview...e9b&pId=356552
Grace went on to remarry to widower Mark Unwin in 1827:
https://www.ancestry.co.uk/imageview...b4&pId=1433465
Looks like they had one child bap before the marriage:
https://www.ancestry.co.uk/search/co...38a388f287c24b
Ooo, no, maybe not as there's a Mark Unwin marrying another Grace in 1825:
https://www.ancestry.co.uk/imageview...59&pId=4168265
That's what comes of getting complacent because the name combinations seem uncommon!!
There's only one obvious death though, so I'm wondering if there's any mystery or just that I've not looked thoroughly!
Grace Unwin Burial abt 1784 5 Dec 1847 St Mary, Islington, Islington
I think that's the right Grace as this is her in 1841 with two of her sons from her first marriage:
https://www.ancestry.co.uk/imageview...n&pId=15338093
Of course I didn't think to see if there's an alternative route forward for your Birmingham-born Joseph as I was too busy with this one!!