OK not sure about the deal with the numbers but after some looking around the 1606 was made in 1985 and 1986. The graph below shows the serial numbers per year for the 1606.
Using those serial numbers on Cubcadet.com's parts site it looks as tho the shifter parts are used on:
1050
1604, 1606, 580, 582 and 1806
The listed charts will help you.
Serial numbers:
1606.jpg
Models that share the shifter parts and their serial number rankings:
1606a.jpg