Johann Heinrich Eberlein, my 5th great grandfather, is the earliest of my Züttlingen ancestors that I have been able to identify. I have not been able to locate a birth record for him in the church records, although the death record suggests that he was born in 1696.
Thanks to Bursarius from the German Archive forum on Familysearch.org for helping me with the word variant and abbreviation that I was not familiar with.

Evangelische Kirche of Züttlingen (OA Neckarsulm), Kirchenbuch, 1619-1938, Family History Center film #2271090. Death record for Heinrich Eberlin, June 1736.
Transcription
MDCCXXXVI
Heinrich Eberlin, Bürgerl. Innwohner [variant of Einwohner] zu Züttlingen starb d. 16. Juny, u. wurde d 17. ejusd. begrab. 40 Jahr weniger 4 monath.
Translation
Heinrich Eberlin, citizen and inhabitant of Züttlingen, died 16 June and was buried on the 17th of the same month. Forty years less four months.