(I gotta run now, but here's some more to work on...)
The church records from Immenstaad are online! However, there's no general index; you just have to hunt through the annual indices. The Rebsteins seem to have been Catholics back then, or at least the records are listed as Catholic.
This is the baptism record of Johan Baptist Rebstein, born 06 Jan 1839, your John's father:https://www2.landesarchiv-bw.de/ofs21/bild_zoom/zoom.php?bes...
You set "Zoom" to 100. His record is on the right page, number 2. On the left page, under "R", you can see how they wrote Rebstein (the third through sixth names)
To look at the rest of the books, insert Immenstaad into the box "Suchtext" at https://www2.landesarchiv-bw.de/ofs21/olf/suche.php?bestand=...
These researchers have a good deal of info on the Rebsteins of Immenstaad in the 1600 and 1700s. You can try emailing them, although they might not speak English.
Winni Weigelt, firstname.lastname@example.org
Juergen Weigelt, email@example.com
Friedrich Mussler, firstname.lastname@example.org