The study looked at the effect of being eligible for a vaccine and the results were clear. (see chart below the fold here: https://erictopol.substack.com/p/the-shingles-vaccine-and-re...)
There was a hard age cutoff in the UK study. Above a certain age, you weren't eligible. Below it, you were. People who were born in the "can get the vaccine" group have markedly lower rates of dementia. People in the "too old" group have higher rates. It's one of those studies where you don't even need to look at the p-value to see the difference.
I'm very open to being wrong about this!