the sun - How much of the ambient radiation on Mars is arriving line of sight from the Sun?

Besides solar energetic particle (SEP) events, it's mostly (almost isotropic) galactic cosmic rays (GCR). GCRs may cause secondary radiation by interaction with the atmosphere or with rock. The smaller the solid angle of the visible sky, the smaller the mean galactic radiation dose. On Mars you get additional shielding by the atmosphere, hence dependence of the atmospheric pressure. More detail in this paper.
Shieldings from SEP events should be rich in protons, e.g. water or food, or you need to go deeper into underground, as soon as a SEP event is detected.
GCRs are partially shielded by the heliosphere. Hence solar maxima protect partially from GCRs, but SEP events get more likely during solar maxima.
Since GCRs are unpredictable, and SEP events can be detected, for solar maxima, protection strategies resultng in an overall reduced radiation dose can be elaborated.