Is it possible for total solar eclipses to happen in the same location in the sky on a regular basis?

In my conworld, there are going to be multiple eclipses a year (like it is on Earth), but I want a total solar eclipse to happen regularly at the same location in the sky (or at least pretty close to the same location). Specifically, once every 1,296 years, on the New Year, during sunrise.

**Context:** I might have placed this in a space related to, well, space. However, since this is going to be deeply connected to cultural beliefs regarding the cyclical nature of time, I felt that it was fitting here.

The cycles are related the number 36 (expressed in their base 6 number system as 100). This number is associated with completeness and perfection. Every 36 years, the solar year and lunar year align, and great celebrations are held on every 36th year. A period of 36 years is called a "Jubilee Cycle."

36 Jubilee Cycles is called a "Great Cycle," and is the period of 1,296 years I mentioned.

The idea is that they believe that their deity Mān dies and is reborn on the first day of each Great Cycle, and so I figure that a total solar eclipse at sunrise would be a great way to signify that.

Is it reasonable or realistic for such an eclipse to happen in such regular intervals? _Unlikely_ probably, but I still want to entertain the idea if possible.

If the information helps, the moon (there's only one moon) orbits the planet once every 40 days. It is slightly faster than this, and as such drifts by 40 days every 36 years, hence the solar-lunar alignment I mentioned in the third paragraph. And this eclipse will pertain to a single tropical island nation (so the whole world probably won't see this). The axial tilt is 22.4.°

Basically the standard of realism I'm going for is that I want my world to technically be _possible_ (so no magic), but not necessarily the most _likely._ But I want to make sure that this thing I'm thinking of is possible within the parameters I've set for my planet.