Left side headlight bucket wiggles when lights are on.

Common. Not worth chasing down unless frankly unstable.

 

Likely the nylon bushings in the hinge.

 

There is a rubber end stop bumper piece that should be adjusted into slight compression to minimize the wiggling in the up position -- either item 8 or item 26 here (one is for "up" and one is for "down"):

Ferrari 348 (1989-1992) Parts : Table 129 - LIGHTS LIFTING DEVICE AND HEADLIGHTS

Check that adjustment (or lack of adjustment ) first...