"Alan" wrote

It appears that one can then fly at night with a private (with a
medical).
Without a medical, it appears much muddier.

It isn't muddy in the least bit. Without a medical, a private holder is a
light sport pilot. That's all. That means NO night flight, period. At
least not legal, that is.

What can a private pilot
without a current medical do in an LSA that a sport pilot cannot?

Not a durn thing, 'cause he is a sport pilot, the second his medical is out
of date, as long as his medical was not turned down, denied, or how ever
else you want to say it.

The plane and all of its components (including the engine) must be
certified
for that as well. It appears that the common versions of the Rotax engine
are
prohibited from night or IFR use by the instructions from Rotax.

True, the plane must be equipped for night flight, but most that were
designed as an original European microlight are. I won't say real airplane,
but if it has a real fuselage, and was not originally made as a US
ultralight, chances are that it is OK for night flight. As to what a
"common" Rotax is, you got me guessing. The Rotax 4-strokes are available
certified or not, but the only visible difference is the letter in the name,
and how much documentation comes with the engine, and of course, the cost.

But again, you 'gotta have the medical to fly at night. Cut and dry.
--
Jim in NC