Hi Larry

Dust clouds or sun shields are a bit too intelligently placed in either scenario to be credible ideas - the binary companion causing precession is already a stretch according to most astrophysics ideas.

On a 24,000 year orbit the companion only goes out to 1600 AU (a = 830 AU) at most if it's a brown or red dwarf. A 9 solar mass black hole would go out to maybe 3500 AU (a = 1795 AU), but then it's not visible anyway.

Any spherical obscuring dust cloud would've collapsed onto the star or dispersed by now. A thick dust disk might work - imagine a dense asteroid belt grinding itself to dust close into the star. But it would need to be almost edge on to our line of sight to cloak the star.

Hmmm... if it wasn't and was about an AU across then at perihelion (100 AU) it would be an incredibly striking sight, an ovoid with a star-like centre. Dare I say it... the Eye of Ra.

Adam