That's a good one. A party slot is only empty if a flag is set. The function key code doesn't check for the flag and neither does the sing function. It looks like the function keys will also work if the bard is dead, stoned, or paralyzed too.
Confirmed. Dead bards can still play long lasting songs if you use the function key. Although I'm not sure what paralyzed is.
I guess this bug isn't particularly useful in normal play, but there have been times when my party was almost wiped out, including all the casters and the bard, when the remaining melee characters were trying to get out of the dungeon without a light. It would have been easier if I had known the dead bard could just play the light song.
Or maybe coldfoxred could use this as another exploit in his speed run. Give the dead bard a bardsword or lak's lyre, and you have unlimited long lasting songs.