Technique for folding sparse event data in order to detect an underlying periodicity?
While this is not exactly how folding works, one-dimensional data encourages trying some simple statistical tallying first.

What very easily reveals those periodicities is just tallying up the deltas, with an appropriate fuzziness for what periodicities are relevant:

Deltas

[0, 9308, 28857, 36709, 28857, 9308, 28858, 36708, 28858, 9308, 28857, 36708, 9309, 19549, 9309, 28857, 36707, 9310]
Already here, some patterns should be apparent. But we have some extra information that could be used to filter out the short period noise.

Rounding at an appropriate sampling frequency

Earth transits aren't going to happen every day. If there was an Earth transit yesterday, it can't happen again today, or next day, or even the next month. In fact, we know they can only happen once for every synodic period of Mars-Earth (780 days).
To not miss out in any &quot;legitimate&quot; part of the signal, we should sample at at least twice of that rate. &quot;one year&quot; happens to be pretty close to half of 780 days.
The periodicity is then readily visible:
[26, 79, 101, 79, 26, 79, 101, 79, 26, 79, 101, 26, 54, 26, 79, 101, 26]
Which also reveals an even higher extra periodicity of about 206 years.
With a strong 206 year periodicity found in a set of events only covering a little over 400 years, there's not enough data to with any certainty detect any higher order periodicities that that.