Tackling another dead end, Peter Hansen Bech, born about 1809. The first concrete record we have for him is his arrival in Mellerup Sogn, late 1837. The tilgangsliste entry is here: https://www.sa.dk/ao-soegesider/da/billedviser?epid=17125184#166708,27994033
-- as you can see, he is only listed as coming from Randers. The entry above his (Mette Johanne Christine Nielsen) is his future wife; they would marry December 11, 1837, with their son Jens being born December 26th.
Bech is probably a tilnavn, so he was likely born Peter Hansen. The census records from 1840 on list Horsens as his birth place, but of course that's not very helpful because there are a few possibilities. He was a sailor.
I know that sometimes the notes in the final column relate to vaccinations, and there is a date of 30 August 1812 there, but I can't read the rest. I would appreciate help in deciphering the last bits of this record and pointing me to where he might have come from -- either immediately before Mellerup, or further back.