Stick in the mud
A narrow-minded or unprogressive person; one who lacks initiative
The figurative phrase 'stick in the mud' derives from the imagery of someone whose feet are stuck in wet clay and is unable to progress. It was preceded in the language by earlier versions, for example 'stick in the briers, clay, mire' etc. These were usually applied to people who remained in a difficult situation, either by choice or because they were stuck.
Thomas Cooper's Thesaurus, 1565, included an example:
They beyng accused of extortion and pillage were in muche trouble, or stacke in the bryars.
Only 'stick in the mud' has lasted. The first citations that I can find that include that are from the 18th century. The London newspaper The General Evening Post printed two examples in 1733. Firstly, on of 15th-17th November:
George Sutton was Yesterday before Justice De Veil, on suspicion of robbing Col. Des Romain's House at Paddington. The Colonel was in the Boom with the Justice, and no sooner had Sutton entered the Boom, but the Colonel said, that is the Man that first came and seized me with his drawn Sword in his Hand. The Justice committed him to Newgate. At the same time James Baker was before Justice De Veil for the same Fact. The Colonel could not swear to him, but the Justice committed him to the same Place with Sutton. George Fluster, alias Stick in the Mud, has made himself an Evidence, and impeached the above two Persons."
And again, on 8th December 1733:
John Anderson, Francis Ogleby, and James Baker, alias Stick in the Mud, for breaking open the House of Mr. Thomas Bayner, a Silversmith, and stealing thence Plate to a great value.
It is clear from those extracts that 'stick in the mud' was used as a nickname and we can reasonably assume that it indicated a particular character trait of the person so named.
The term 'an old stick' or 'odd stick' is, or rather was as it is falling out of use now, used to described elderly and mildly eccentric characters. That isn't the source of 'stick in the mud' but may well have derived from it. The first use I can find of that term is in John Hotten's Dictionary of Modern Slang, 1859:
'A rum' or 'odd stick', a curious man.