I would not be surprised if there _was_ a heck of a big effect -- something along the lines of "how bad the vaccine side effects hit you is strongly correlated with general health such that people who are less healthy tend to have worse side effects, and people who have particularly bad side effects from their first dose are less likely to get a second dose".

I don't have time to look into it right now, but if that were the case we should expect the mortality rate for single-dosers to go up two weeks after their first dose in countries with a two week gap between doses and twelve weeks after their first dose in countries with a twelve week gap (i.e. people in the 12 week gap countries who are 6 weeks after dose 1 should have much lower mortality than people in the 2 week gap countries who are 6 weeks after dose 1 and have not gotten a dose 2, even after controlling for age and comorbidities).