Ideas:

1. This glyph type, which I think of as 'the tired old bird', is a contrast to the straight standing splendid bird in showing much variability in its form and probably not all these variations are due to the writer having attatched signs. Therefore I believe that the bird with hanging head is not directly referring to the Sun God (or to any other Great Power).

2. The great variability in appearance of the old bird makes it difficult to distinguish what is a sign and what is just a normal variation for this type of glyph. However, I think (after having made a special study of this type of glyph in Large St Petersburg Tablet) that there is a sign in this glyph, a sign in the form of showing the tail feathers. (Possibly there is also a sign in the form of an unusually tight bend of the neck.) The old bird here in Sunday is - I think - an indirect reference to the Sun God.

3. Why are there five glyphs in one text (H) but only three in the other (P)? One possible answer is to say that two glyphs corresponding to Ra (or rather its equivalent in the Rapanui language, Ra'a) and tapu are found in H but not in the corresponding place of P. The pair of added glyphs in Large Santiago might be referring to the Sun before and at noon, in which case we can associate the sun-boat with dawn and the old bird with sunset.