Setting the player position while the iTunes player state is paused resets the player state to stopped and resets the player position to 0.
tell application "iTunes"
play -- initialize the state to Play
pause -- put iTunes in Pause mode
set player position to 5
log (get player state) -- will be stopped
log (get player position) -- will be 0
Attempting a workaround, I found that as long as the track isn't paused, the player position can be set.
This did not occur in previous versions; setting the player position while paused would, as expected, move the play head to that position. In fact, Needle Drop uses a variation of this to begin playing a track at a user-set start time. Needless to say, this won't work with iTunes 12.4. (Hat-tip to Correspondent Rob Robinson.)
[UPDATE: Needle Drop v5.3 addresses this issue.]
[UPDATE ALSO: this issue is fixed in iTunes 12.4.1.]