To orient the ship to face the sun steadily, try the vector of the ship to the sun, and cross that with the velocity vector of the earth relative to the sun (not the ship relative to earth).

Alternatively, try the velocity vector of the ship relative to the sun. This would have a slight daily wobble to it, which might be hard to notice visually. The wobble would depend on its inclination and eccentricity, and even with a circular equatorial orbit it would still wobble.

Another idea is to create a vector to a distant star, such as the north star, or the whole star field, or the cosmic microwave background radiation, and use that. That would be the least wobbly solution because even the earth gets pushed around by other planets.

I don't know which might yeild the best results for your application.

To orient the ship to face the sun steadily, try the vector of the ship to the sun, and cross that with the velocity vector of the earth relative to the sun (not the ship relative to earth).

Alternatively, try the velocity vector of the ship relative to the sun. This would have a slight daily wobble to it, which might be hard to notice visually. The wobble would depend on its inclination and eccentricity, and even with a circular equatorial orbit it would still wobble.

Another idea is to create a vector to a distant star, such as the north star, or the whole star field, or the cosmic microwave background radiation (UPDATE: the CMBR is nonsense, see comment), and use that. That would be the least wobbly solution because even the earth gets pushed around by other planets.

I don't know which might yeild the best results for your application.