Sometimes, a name tells you a lot. Shining flower beetles are shiny, they can be highly abundant on flowers, and they are, indeed, beetles. Some of their relatives are called shining mold beetles because they are abundant on fungi. All are in the family Phalacridae.
These beetles are also small, which probably makes the mold beetles easy to overlook, but the flower beetles are right there on top of the flowers, really hard to miss (if you stop to look). They are especially shiny in sunlight, and their brown color contrasts with the bright color of the flowers. They appear to be bite-sized for a bird, but I have never seen a bird grab one (though it would be so quick that the chances of seeing it are tiny, just like the beetles).
In the cool of the morning, the beetles are mostly between the flower heads, an indication that they spent the night there. In the middle of the day, they are often on top of the flowers, heads down, giving every indication that they are finding something on or in the flowers to eat. Their mouthparts probably cannot reach nectar, but pollen and tender floral tissue are right where their mouths are.
Grass-leaved Goldenrod (a necessary digression)
Decades ago, grass-leaved goldenrod was classified in the genus Solidago (S. graminifolia), but taxonomists decided that it, and similar species, should be in a separate genus, Euthamia. When it blooms, the flowers are yellow and look a whole lot like those of any other goldenrod around them.
As you can see in the picture, shining flower beetles congregate on E. graminifolia flowers as soon as the first ones bloom. They spend little time on unopened flower buds, but can’t seem to get enough of the yellow blossoms. As far as the beetles are concerned, a goldenrod blossom is a goldenrod blossom, no matter how the plant is classified.
Where do shining flower beetles spend the winter? Good question. I would guess that the females lay eggs somewhere on, in, or near the plant, where the eggs remain dormant until the spring. The larvae live among flowers, but I don’t know whether the eggs wait to hatch until goldenrods are available. I suspect not, and I suspect that they have more than one generation a year. It would be interesting to find out.