I had mentioned that in the 1940 edition of "Familiennamenbuch" Ganterschwil SG was mentioned as pre-1800 place of citizenship for Klausner - but no longer in the 1962 edition (basis of the online edition).I read in the a post that you wrote, family Klausner early died out. I have Anna Maria Klausner born about 1840 who married Johann Hagmann born 1835 in Sevelen. Is it possible to find out about her Klausner line?
But ... as you already know from the topic Hagmann of Sevelen, Anna Maria Klauser (not Klausner!!) was born 1833 (not about 1840) in Flums as daughter of Jakob Klauser and Cathrin Bärtsch. She was catholic - opposed to her reformed husband Johann Hagmann.
BTW - the Thommen collection is now online
According to the baptismal entry of 02.02.1833 the family lived "im Dorf", one of the three communities forming Flums. Jacob Klauser and Catharina Bertsch got married in Flums 11.04.1826.
In this time frame one should also check the Bürgerregister (right side): Jacob Klauser was born 08.06.1798 ... same image, left side you find his parents - Johannes Klauser (1769-1849) and Marianna Oßlati (1773-1841). Their parents are mentioned by name, but without data - Bürgerregister don't go further back.
Next step would be to search the church records: all older church records of canton St.Gallen are online - see here for Flums.