2003 P71 clicking noise while slowing

I have a 03 Crown Vic P71. I just purchased this a couple of weeks ago. I have noticed a very slight clicking sound and cannot pinpoint it. I am certain it is not the brakes.

While accelerating the clicking goes completely away. This clicking only happens while non-accelerating and slowing down for a stop. The second I accelerate the noise disappears.

I thought it was the belt tension pulley not putting enough tension on the belt but I replaced that last night and still hear the clicking.

The sound is almost like if you put playing cards that rub the spokes of a bicycle. The clicking is very slight and most people probably wouldn't even hear it. I have excellent hearing so it stands out like a sore thumb to me.

Trying to determine where it is coming from, to me it sounds like maybe the drive shaft or maybe somewhere around where the transmission is located. Not sure though.

Thank you,
Scott

My mechanic diagnosed the problem. It took a long time to narrow it down.

Turns out to be the rear end differential. There is a slight amount of play in the gears and pin. While the car is on a lift with the drive shaft removed and rear end exposed we were able to reproduce the noise by rotating the wheels.

Just the parts alone are going to cost me $1500. Shoot!!!!!