The script does work, but when you try to quit SheepShaver the MacOS asks to shut down the emulated machine. If you would quit SheepShaver without shutting down the emulated machine first, it would be like a hard shutdown that could result in file system corruption on the MacOS volumes.
You could use a script like this one below. It brings SheepShaver to the front, quits SheepShaver, and (after a delay to allow for the dialog to appear) presses Return to shut down the emulated machine. If a delay of one second is not long enough on your machine, you can make it two seconds.
tell application "System Events" to exists process "SheepShaver"
if result is true then
activate application "SheepShaver"
quit application "SheepShaver"
delay 1
tell application "System Events" to key code 36 #return
end if
Like I have already said a few times ... Ronald, you are a genius. It works perfectly. I will include that in a background routine, and it should do the trick. Leaving SS running prevents my screen saver to launch and the monitor always stays bright.