FWIW, the Google Search pronunciation guide[0] says Guassian like "gouse-ian", which is the only way I've heard it pronounced (US east coast). It's also what I see as the phonetically-written pronunciation when checking a couple dictionaries[1], and this English blog post[2].

[0] https://www.google.com/search?q=pronounce+gaussian&rlz=1C5GC...

[1] https://www.dictionary.com/browse/gaussian

[2] https://painfulenglish.com/2014/01/26/how-to-pronounce-gauss...

I am sure that it's just a case of people having read the word and never heard it spoken.

Huh. Must vary by community. I've only heard them pronounced in concordant ways, and closer to your first.