There is a Custom Styles category in panels in which you can set custom StyleBoxes.
I tested changing the
Panel one with a new StyleBoxFlat, which changes the color of the panel but not dynamically.
You can set the
Bg Color of the StyleBox but it doesn't update in the editor, which is not handy :p
If you run the scene however, you'll see the color.
When it's about to do that in code, I managed to get a blinking panel with this:
var style = StyleBoxFlat.new()
# The Panel doc tells you which style names there are
# Some basic code animation
var color = Color(0.5*sin(OS.get_ticks_msec()/100.0)+0.5, 0, 0)
# Don't forget to update so the control will redraw