Only just found your query about John Graham (1811?-1869).
I have been researching the Birmingham Town Council in the 1870s and his name cropped up, through he was one of the quietest members there. He was a Councillor from 1863, returned twice for St Paul's ward before resigning just before his death.
He has an obituary in the Birmingham Daily Post for Saturday 25 December 1869 (published Christmas day?!), which says he was in his 60th year, came to Birmingham from Scotland in 1843, was prominent in the Carr Lane Presbyterian church and a founder and director of the Birmingham Joint Stock Bank (merged with Lloyds), and with a son (Walter) as merchants on Ludgate Hill. Touchingly it says "many a deserving poor family will miss [his] benevolence... [which] made glad their cheerless fireside". (I love the Victorian gift for written language and their unforgiving paternalism...).
I, too, have found him very elusive in the Censuses. I am sure you have found the obit by now, but if you have more information about him to share, I would love to hear it.
AlexCrewe