I tried to find out what towns those surnames were common in.
To start, I entered the surname at Geopatronymne.com, which looks at how common a surname was in records from 1891-1915. There was no result for , but here's the result for STOCKLIN:http://www.geopatronyme.com/cgi-bin/carte/nomcarte.cgi?nom=S...
It was most common in Haut-Rhin and by clicking the link for that department, it said it was most common in Oberdorf, Mulhouse (a major city, so this doesn't mean much), Bourgfelden, Huningue, Rixheim. The easiest way to search for someone is by using the "decennial tables" for the town, which index the births, marriages, and deaths in the town for a 10-year period.
The record (in case the link doesn't work) is page 25 of 30 of the Oberdorf Tables Deccenale for 1863-1892 (the archives combined three TDs back-to-back as a single catalog entry). I checked the deaths (S is on page 29) and there was no matching death (just to make sure she didn't die as an infant...at least in that town).
Here's the link to the birth certificate (left page), which has a notation stamped on it that this individual died in Altkirch on 11 March 1979:http://www.archives.haut-rhin.fr/ark:/naan/600bdc6cd6
If the link doesn't work, that is page 64 (of 109) of the Oberdorf births/marriages/deaths records for 1883-1892.
I can read French very well, but not German and just have to type the words in Google Translate to see what they mean...and I still struggle to decipher the handwriting. German used a different handwriting than English or French, called "Kurrentschrift", until the mid-20th century. The TD index uses the German style handwriting, but the birth certificate uses mix of Kurrentschrift and English/French-style handwriting, so hopefully someone else can help decipher/translate for you. Here's a sample of German handwriting letters: https://commons.wikimedia.org/wiki/File:Deutsche_Kurrentschr...
The father's name is "L??? Norand Stierlin" and the mother is "Catharina Stierlin born Allemann". Both are Catholic.
The digitized records available on the Haut-Rhin Archives' website don't extend into the 20th century, unfortunately. The neighboring Bas-Rhin department (were I'm used to researching genealogy) has digitized records to 1912, so I assume that the Haut-Rhin archives has records at least until 1912. For the 1979 death record of this individual, you'd need to contact the "mairie" (town hall). In 2016, Oberdorf was merged with neighboring Grentzingen & Henflingen to form the commune of Illtal. I could not find a website or email address for the Illtal mairie. When I searched for info about how to obtain a death record ("acte de deces" in French), it seems like anyone can request one, without needing to provide a reason (which seems odd, given how Europe treats the right to privacy).
P.S. I have a page on my website that explains the decennial tables and how vital records are kept. It mainly focuses on French-language records up to the time Alsace was ceded from France to Germany, but you should still find it useful. https://alsatiansettlersofshelbyandauglaizeohio.wordpress.co...