The eight weeks is based on:
https://www.medrxiv.org/content/10.1101/2021.05.15.21257017v1
Which is pre-print on a small population sample (172) of only over 80 yo, it's definitely best to wait at least 3 weeks, but anything over two weeks is fine, past that point as long as it's before 12 weeks, you're fine but it's usually the consensus 3-4 weeks is best as then best against covid, all the longer wait stuff talking about sampling error or due to still having vaccine in blood and stuff (be it smaller population, how people react, environemnts, etc.).
From that paper's results:
But again, note no peer review.
Most of the people using 8 weeks as politicians are using it so they can get more first doses out/stretch out the time in which people need the second dose.
6 weeks is good to go, anything post 3 weeks is fine, the response difference isn't that major.
I'd most likely trust the CDC:
https://www.cdc.gov/coronavirus/2019-ncov/vaccines/second-shot.html