There is a big difference between the two dwarfs. White dwarfs are the
remainder of moderate mass stars and are not accomplishing fusion
although they emit mostly in the visible until they cool.

Brown dwarfs are puttering along with D-D fusion and not much else.

I'm guessing at the rate brown dwarfs burn deuterium, that they stay
steady state for most of the life of the universe. The fusion is not
supporting any type of gravitational collapse so even when the D-D reaction ends, there is no major structural change. Maybe convection will grind to a halt when it cools enough.

But it still never supported fusion on a major scale. It's just a toasty warm super Jupiter. I'm not sure I agree with you that a BD would
be visible. Now, you could change my mind if there are visible spectrum
pictures from a telescope you know of. I see it having the same spectrum of an electric stove burner just as it's starting to become visible and your not really sure if it's on or if your seeing reflected light.

White dwarfs - has been
Brown dwarfs - wanna be

Thats my story and i'm sticking to it.