You need to inspect the rotating assembly and determine if there is any binding in the linkage for the light pod. After that, remove the actuator.
Here is the good/bad/ugly of these things. They can be rebuilt to some degree. Your 85 motor is much different than the 88-96 design.
You can drill out the rivets and open the housing. Once inside you will find your lower big gear center is chewed up. It has three hard rubber spacers in there that get torn up over time. Look in Mid America, etc. for the rebuild "brass" gear set and replace the gear mechanisim. When you reassemble, just get some stainless bolts and locking nuts to reattach the housing pieces. You will want to apply a fresh RTV or silicone sealant to the two halfs to keep the moisture out.
Next, there is an access panel on the side of the actuator with four 7mm hex headed screws. Remove that panel to expose the switching mechanism. Get some good electric contact cleaner spray and clean all the contact points, and observe is any have just melted away over the years. This is where you can and might get lucky swaping these parts for some bone yard Firebird and Fiero pre 1987 headlight actuator parts.
Sometimes just cleaning them does the trick.
Final point. The Pre 88 Vette actuators depend on a series of relays to make it happen. These can stick, fail, etc. These relays are not expensive and can be matched up at your local Napa or auto parts dealer. It is not a bad idea to replace them while you are in there.
If all else fails, you can always upgrade to the 1988-96 design. Mid America sells a kit for about $550, and or you can shop e-bay or the Corvette recyclers for later model units. You will need the single control module, headlight assemblies, and wire pig tails. Your headlight switch remains. If you have a buddy with a 88-96 Vette, you can just probe out his harness to determine where to hook the power, ground, up/down signal wires to finish the job on your 85. IF you upgrade you will be much happier with the sound, feel, and action of the later model units.
Hope that helps!