... or you could try taking a completely different "day of the month" number and looking for a pattern on that and you will probably find one if you look hard enough. What does it prove other than we can impose patterns if we want to? If we took a lot of people, and looked at their a persons day of birth and the age they were when their father died, some (a small number) will be the same, and some (many more) will be different. So what?
There will be a peak of correlation for people born on the day which matches the curve (average life expectancy - average age of father at birth).

Since
- the average life expectancy in Europe or North America since WW2 is in the region 65-75 (source),
- and the average age of fathers (in the UK since 1980) is around 30 days (source)
then the most common "age at father's death" would be 40 .... what exactly is the 40th "day" of any month?
At the extremes, some people will be -9 months when their father died, and some will be in their 70s, there will be people of all ages in between, but virtually all will not show any such link. We can move on to every other co-incidence you have listed so far, but that's all they will be shown to be ... a coincidence. This is pattern matching. Get over it.