Thanks so much, Michael! I will have to check out these links. Naturalization paper searches keep bringing us to the wrong Paul. Haven't checked Pension papers. Would there be pension papers simply because we found a draft card?
Amazing, but just last night I found this on familysearch.org. This matches the birthdate on one of the photos.
"Joh. Fridr. Paul
Germany, Births and Baptisms, 1558-1898
birth:22 AUG 1822
christening:25 Aug 1822SANKT MARIA SALOME KATHOLISCH,OVENHAUSEN,WESTFALEN,PRUSSIA
parents:Heinr. Paul, Justina Wassmuth
name: Joh. Fridr. Paul
baptism/christening date: 25 Aug 1822
baptism/christening place: SANKT MARIA SALOME KATHOLISCH,OVENHAUSEN,WESTFALEN,PRUSSIA
father's name: Heinr. Paul
mother's name: Justina Wassmuth
indexing project (batch) number: C94199-2
system origin: Germany-ODM
source film number: 1056109"
I am not exactly sure what to do from here.