Habitat Precession

I need a little help with some minor points about orbital precession
around the sun.

Many of the habitat designs (O'Neill Cylinders, Stanford Torus,
Bernal Sphere) design the radiators so that they are edge-on to the
sun.

I can see how this makes sense if the habitat orbit is similar to a
planet's.

If the orbit is around a point at 90,000 miles from the L5 point, or
is a 2:1 resonant orbit that ranges from 100,000 to 200,000 miles
from earth and has a period of two weeks, then will orbital
precession still be as exact?

I guess the central question is can the habitat precess so exactly
as to design the radiators edge-on to the sun and is this precession
independent of the habitat orbit? I'm inclined to think precession
is independent of orbit but would like some confirmation. Also,
would varying gravity encountered along the orbit affect the
automated precession rate of the non-rotating habitat structures?

The orbital mechanics are giving me a headache! I'm trying to
imagine how the forces would be applied when a torus is rotating,
needs to precess with the sun, and is in a 2:1 resonant orbit with
the earth and lunar gravity varying during every two week period.

Or will this not be as automatic for a torus? Will there have to be
a "precession engineer" who'll have to calculate how much to precess
the non-rotating structures of the torus so as to have them be edge-
on to the sun, and execute the procedure with attached drives? If
this is indeed the case, then what effect will the precession motion
have on the de-spin coupler, and the parts of the structure that are
designed for zero-g forces?

I sure hope somebody can set me straight on this!