Ytdyklly

Given a system similar to the Earth/Moon/Sun system, how would one go about making solar eclipses rarer than they are here on earth, but keep new moons similar to how they currently are (or at least similar)?

At first I thought that increasing the lunar tilt from 5 degrees to, say, 10 degrees would help, but there would still always be two "nodes" indicating where solar eclipses could happen on the planet. Even at a 90 degree angle, twice a year, the planet would see solar eclipses. at 10 degrees, new moons would still be relatively as frequent, though at 90 degrees, I don't think there would ever be a new moon.

Is there a way to make total solar eclipses happen infrequently, while keeping new moons frequent? And if so, what variable(s) need to change to make that happen?.

Just shrink the moon by 6%, and there will never be another total solar eclipse, but new moons will still happen as normal. The moon will be too small to fully cover the sun, so there will be partial and annular eclipses, but no total ones. If you still want the occasional total eclipse, make the moon slightly bigger again, so that eclipses are total if and only if it happens to be at the closest point to the Earth in its orbit at the time of the eclipse. We’d still get the same number of eclipses at the same time, but hardly any of them would be total.

Since both the moon and the Earth are in elliptical orbits, the apparent angular sizes of the moon and sun vary. Specifically, the moon varies between 29' 26" and 33' 30" while the sun varies between 31' 36" and 32' 42". You want the moon’s maximum to be just larger than the sun’s minimum, so that there are very occasional total eclipses if we happen to get an eclipse when the moon is at its closest and the sun is at its furthest. So to reduce the moon’s maximum angular size to 31’ 40” you need to make it 5.5% smaller without changing its orbit.

Keep sun and moon sizes, make the orbit of the Earth around the sun more excentric and with a smaller mean distance.

The new moon is unnafected, but full solar eclipses will only happen if the eclipse happens together with the Earth's apoapsis, or close to it. And that will only happen during a few specific days of the year. Any solar eclipse far from the apoapsis will be partial.

That also implies shorter years and a whole different set of conditions on the planet that might not be compatible with life as we know it, though.

Why not make the moon's orbit precess? If the precession chases the sun (from the perspective of earth) while staying a bit off from it, you could keep new moons as common as always and eliminate solar eclipses altogether.

If you made the presession not quite at the same rate as the sun, you could also cause large periods without a single solar eclipse, followed by a period where a solar eclipse happened every month (which, from a story perspective, could be interesting).

Alternatively, if you had the moon precess in the opposite direction of the earth's movement around the sun (and depending on the length of your lunar month vs solar year), it may be possible to have the moon 'miss' a solar eclipse except for once every few hundreds of years.

At 90 degree inclination, you could still get new moons near the nodes where the inclination of the moon's orbit with respect to the line from the planet to the sun is low.

The presence of nodes in the planet's orbit where the inclined orbital path of the moon intersects a line pointing towards the sun, however, is not itself problematic, because it is not itself sufficient to cause eclipses. And that's a good thing for you, because it's a simple geometric fact that you can't avoid them. In order to get an eclipse, the moon also has to actually pass through that intersection point during the brief period when it exists every half-year. As such, a very simple solution to avoid ever having an eclipse presents itself: just tweak the moon's orbital period so that it forms a simple integer ratio with the year, such that the moon is always in the same phase on the same date every year--and then just declare that the phases are such that you never have things line up for an eclipse.

Instead of one moon which is just big enough and close enough to cause a total eclipse whenever it intersects between our planet and our sun, why not have several moons which are each either smaller or more distant such that no single moon can produce a full eclipse.
New moons would still happen and would actually be much more common than Earth standard, but total eclipses would only occur when all of the moons simultaneously entered the intersection point, each blocking a portion of the available sunshine and collectively blocking it all.

Resonance. Pick a ratio of the lunar orbital period to the solar orbital period such that the moon normally in the wrong part of it's orbit when it's both directly sunward and in the plane of the ecliptic. The bigger numbers you need to use to express the ratio the longer it will be between eclipses.

Unlike normal planetary resonance orbits no force will maintain this or cause it to come into being but as the moon slowly spirals out there will be a time that it happens naturally. You'll have to adjust the size of the moon so it provides a total eclipse at that distance from the Earth.