This can be fixed by stretching out a solenoid spring on the power cord
side of the printer. The solenoid acts as a clutch to stop the spinning
developer actuator at the right spot.
Below steps are for the CLP-300 which has the same Imager/Developer. It's just a bit more involved taking off the top in the CLX-3160.
Open up the right side (power cord side) of the printer (take off top
cover, then take off side cover). Then, find a solenoid (little metal
square) that touches the white plastic vertical spur gear. Take the
spring off the solenoid. Now, put the spring back on - only this time
you will attach one anchor point to the middle of the spring as to
pre-stretch the spring for more tension.
The problem is that the spring gets weak over time / the cogs round out
over time and the solenoid finger is overcome by the spinning cogs, and
resulting in selecting the wrong developer.
More pictures of the solenoid on Facebook: