The DIN socket/muting relay assy (8005044 on wiring diag) is secured by a single screw and two curved tabs that hinge up/out of the base after releasing the screw. If the looseness is from the screw, the entire assy will be loose. If not, then something about the socket inside is wrong. This should be checked, especially given your complaint.
Looking at the the long brass worm-screw from the normal/front perspective, the sensor is at the right end; there is a shutter-wheel on the end of the screw. The sensor is U shaped, with a light source and a photo-sensor. The adjacent motor and belt turns the shaft and the sensor sees each slot in the wheel; the signal goes to the processor which is the brain; it counts and keeps track of velocity and position of tonearm.
The sensor, light source, and light slot for the tonearm angle is in the under/front area of the tonearm assy or tonearm carriage as I call it. As the arm moves out of tangency, the shutter diminishes the light to the sensor and the processor responds by (slowly) turning the arm motor. AFAIK, the 8000/2 B&O only move forward in the groove; I think my Yamaha PX-2 is bi-directional.
A good thing for you to do would be to take your "parts" unit down to the point where the entire upper case and covers are gone. You can now lay a piece of corrugated cardboard over the area where the main circuit-board will naturally want to return to; this will insulate it from the electronics and steel base below it. Remove the control pad and the transformer from the case. Reconnect the ribbon wire for the keypad (pay attention to how it should be and don't get the ribbon-wire 180*/backwards!). Plug the transformer to the main board being careful that it plugs into the terminals correctly (the terminals are equip-distant so you can plug it together incorrectly when the case isn't there to only allow the right orientation. In this configuration, you can put a disc on the platter and play it-even through the stereo. You can swap things around to see if they work or not. Everything is pretty accessible for doing electrical tests. The voyages are low enough ton not be a safety worry. You are better off working on this unit and bringing it to life and heath. Once done, you will have a much clearer sense of the bigger picture and be ready to move on to the others, otherwise, I'm afraid they will all become parts units!
The spring's purpose is proper electrical engineering-to bring the major metal parts of the unit to a common ground plane, which includes dissipating static among other things.