For this use, "gossamer thin" is unlikely. You want to control where you point the mirror, it needs a structure that not only doesn't flop around when you torque your spacecraft, but also doesn't have surprise vibrational modes that squeeze and expand the illumination zone.

(Things I'm learning while researching what is now looking like an eight thousand or more word blog post about why a different space thing, data centres, is also not a good investment; my guess is this would be less of a problem if you used mirrors like this to cool the earth by reflecting sunlight away instead of towards).