Did dwellings on homesteads have to be a certain size?

In looking at the language of the 1862 Homestead Act  https://www.ourdocuments.gov/doc.php?flash=false&doc=31 and the 1916 Stock Raising Act https://www.loc.gov/law/help/statutes-at-large/64th-congress/session-2/c64s2ch9.pdf neither of these two documents makes any mention of dwelling requirements.    Because of this the GLO issued sets of Instructions for the Homesteaders at varying times during the 19th and 20th Century.  These would be the set of instructions that the GLO and the Homesteader would use to make sure a parcel of land reached whatever the current threshold was to receive a patent.  As with most thing the law changed over time. The instructions were issue by both the GLO and published in the Federal Register.  An example of one of these instructions can be found on the Hathi Trust website  https://catalog.hathitrust.org/Record/000237462?type%5B%5D=title&lookfor%5B%5D=Homestead%20Laws&ft= .  You can perform a search on the Hathi Trust website for a broader search topic.  Typically they have a digitized version of the document.   Unfortunately, due to sever staff limitations, we cannot undertake the research to find the exact instructions that would have the 12 x 14 requirement but hopefully you can find that from the Hathi Trust documents.

I think you are on the right track about a shared understanding of what is acceptable, at least locally.  I did some more digging and could not find any specific requirements for the size of the dwelling within the instructions or other GLO publications.  Some historical work that I looked at pointed to the the Preemptive Act of 1841 as containing the dwelling size instructions.  Upon review of the record I did not see it.

I also checked with several colleagues outside of NARA who are also land experts.  None of us have found any indication within the GLO's records a uniform size requirement for the dwellings.  The purpose of the dwelling seems to be more that the GLO wanted to see homesteaders put forth a good faith effort to build a dwelling that would be sufficient for the homesteader and their family.

Perhaps size requirement were something informally suggested by staff in the various land offices.  This would be why you might see a similar size throughout a specific portion of the country, but I have not found anything written in the textual record supporting size requirements.