I have the same drive and recently I experienced the same problem.
I backed up the 500gb and took it out to pasture. noticed a lot of read errors when I was backing it up too. was only a USB 2 drive and upgraded to a 3TB USB 3 drive and couldn't be happier.
I don't know why it pulses or won't shutdown properly. really annoying to as all the lights go out in the room everything gets turned off and shutdown but there is this one pulsing light tormenting me.
I think it just means the drive is about to die. $60-120 you can get a replacement that will blow it away.
BACKUP UP YOUR STUFF NOW. That's my recommendation.