You mean Irish Moss? It's not technically moss, and has its challenges. A lot of challenges: https://www.gardeningknowhow.com/ornamental/groundcover/irish-moss/growing-irish-moss-plants.htm

Full sun to part shade only; give it even part shade and it gets leggy. "Late afternoon sun" is not even part shade, really, so I wouldn't count on it doing well.

Regular moss? It's inconsistent, patchy, and doesn't really like sun at all, and demands wet conditions. Nobody cultivates it intentionally.

Clover might do, but does like sun as well. Still, it's cheap and worth a shot.

Nobody cultivates it intentionally. Actually, yes, some of us do grow moss intentionally. Mine really just grows itself but I remove weeds or grass that try to impinge on its' territory. My moss has been the loveliest emerald green this winter.

Yes there are cultivated moss gardens and yes moss will grow in sun.

Mountain Moss -- Experts in Moss Landscaping – MountainMoss

You learn something new every day. :-)

You mow or you weed. If you would really rather be down on your hand and knees doing maintenance, well that is your choice.

Moss needs lots of water. You coukd try a ground cover. Wintergreen might be slow to spread, but I doubt ticks like

"Moss needs lots of water."

Some do....some don't. It depends on the species but there are mosses that will grow in very arid environments as well as those that prefer damper locations. In many cases, a moss lawn will grow with much less water than a traditional lawn would require.

Sorry meant I love MOSS but can’t find how to edit on app