Try this:-

#test open/close animation palette

import poser, time

try:
    poser.PaletteById(poser.kCmdCodeANIMATIONPALETTE).Show(1)
    print "Animation palette opened."
except:
    print "Unable to open animation palette."

poser.Scene().DrawAll()
time.sleep(20)

try:
    poser.PaletteById(poser.kCmdCodeANIMATIONPALETTE).Show(0)
    print "Animation palette closed."
except:
    print "Unable to close animation palette."
poser.Scene().DrawAll()

I found that this appeared to enable/disable the palette rather than open and close it. I suspect that it is going to be far easier to start with a pop up message asking the user to ensure that the palette is closed before running the script.