All that flitters is not a goldfinch

In the late spring there was a beautiful pair of goldfinches that could often be seen around the yard together. The birdfeeder in our youngest ash tree only accepts small birds, and they tended to prefer that one. Since then one of the birds left and the other one has remained. It has a dull coat, but I don't know if that means if it is the female or if the male has lost his bright plumage since the end of mating season. Whichever one it is, it spends much time in the trees or at the feeder by itself, but occasionally comes to peck at our windows. It will flitter at the bottom of the window for minutes at a time, tapping its beak against the glass. At first I thought it was trying to get in, but earlier this morning I saw it doing the same thing to the sideview mirror of our neighbors' Jaguar. I suppose this whole time its been seeing not what's inside, but what's reflected from the outside—namely its own reflection. I think it's a very lonely bird.