Is that the Walvale off ebay from a few weeks back ? Smallish frame, beautiful lugs ? I was after that because Walvale are A) grossly not known as top frame builders of the 70's -80's and secondly they where my LBS (local bike shop).
If ever you want history on the shop etc, just PM me
Now to the matter in hand. As stated by cymbal, it may well be the plastic insert is mis-aligned / not seated properly / missing. I will assume however you would have noticed this part missing since it has the flat notch in to prevent the lever just slopping all over the place.
I suggest it is not the nylon but a brass spacer / shim that fits on top of the assembly at the end just before you screw it all togther. It is this that applies the correct pressure and stops the lever returning to its un-tensioned position. Without this shim, the screw in doodah that holds it all in place will simply bottom out and not tighten, no matter how much you try to turn it.
I have had this problem twice now when fitting what look like simple levers to a frame that had similar type on, but, in 1 case it was that the stack height of the whole lever was slightly different to the older 1's I took off. In short, "the tightening nut is bottoming out on the brased on gear lever thingy (sorry my brain is half asleep)" Either way, it really sounds like it needs a shim/spacer to allow the tightening nut to actually do its job, and not bottom out before it tightens the levers in place.
I can help with this if you're stuck for that part
No charge, just need an address to send to, so PM me if my answer is the solution to your problem and you have lost / misplaced / never had this vital part of C Record GL's. Hope all of this made sense, yours Laz.