Could be the James Rymmer, son of Thomas, who was baptised 30 Aug 1730 at North Meols. There don't seem to be any other Jameses born about that time. His eldest son was named Thomas so it fits nicely.
Edit - I've found a public tree on ancestry which has a transcription of his will, and he is the James Rymer of Birkdale who was buried 9 Apr 1764. The will mentions his father Thomas Rymer and his father-in-law Thomas Rymer.
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