In the absence of an authoritative reply here is my two pence worth.
I can't see why a 2003 seat would not fit a 1999 model and vice-versa.
However, the part number for the 1999 model is 5DM-24730-00-00 and for the 2003 model is 5DM-24730-10-00. There is a considerable difference in the listed price between the two, the earlier one being more expensive for some reason, so maybe there is a difference in the seats that escapes me.
Hopefully some one can enlighten us both.