Ok, so the linear motor for the sleigh is not the culprit. I've put some lead wires on the power to that linear motor, turned on the player, I let it do it's back and forth movement, then I put in a CD, and after the second "click", I disconnected the linear motor....and the click was still there, so now I have confirmation that this indeed has to do with the focusing / tracking mechanism.
Also, this is the culprit that takes the VEE line out of regulation.
Now, if the actual focus coil driver was at fault, it would not move the focus coils up and down at power on, right? And I can clearly see the lens moving when powering up, so my only thought is that the VEE regulator is the guilty party here i.e. D964, Q951.
In light of this new information, I've proceeded to do some measurements on the PNP and the Zenner. The Zenner D964 is a 7.5V one. The measured voltage drop across it is 7.3V, but this drops to 6.5V, not when the linear motor is moving, but only when the focus coil is moving. So, there's something loading it....and it's not the Linear Motor driver, that taps the anode of D964. Also since the Cathode of D964 is connected to the +5V rail, I've measured that also, and during all operations, the 5V rail is nice and stable.
The Collector of Q951 is at -2.36 V (with respect to GND) but this drops to about -1.8 V when the focus coils are moving.
The actual VEE line (which is labeled as -2V on the PCB) sits at about -1.7V, and this drops to -1.13 V when the focus coil is moving. Also, the manual isn't very helpful here, because it gives some wacky voltages around Q951, that have no logic. (i.e. 4 V on the PNP's collector)