I believe the ticking sound comes from the centrifugal switch inside the motor which activates the start capacitor during motor startup and then automatically disengages when the motor gets up to enough speed to overcome springs built into it and open the contacts to disconnect the capacitors. When the motor power is shut down and it slows, the springs should retract the contacts and may get stuck, which may be causing the noise. It may just be dirty, but It may be necessary to replace this centrifugal switch with the proper Leeson part before it fails because the switch protects the motor windings from too much current at start up. I would recommend that you get the specific motor number and contact Leeson for the correct replacement part -- OR -- contact a local motor repair shop and ask what they would charge to repair/replace the switch.
