You are right. I don't need it to function, only need it to cover the truss rod bolt and the two screw holes in the headstock.If I recall correctly, the string clamp with those bridges had a curved underside. It was intended to mount behind the nut on a Fender style headstock.
To be honest, it might prove wiser to forget the clamp and upgrade to locking machineheads.
I agree, but that gap is pretty fuglyHonestly I would just use some locking tuners. I recommend Grover mini rotomatics.
I actually have a set but I think they're opposite to your headstock.
I plan to block this bridge with a piece of wood, so in that case do I need locking tuners or just a good set of regular ones?That might take a Kahler-style behind-the-nut locking clamp, so locking tuners will be just as good. However, those were held with 4 screws. This looks like they put a Floyd-style nut (two screws) behind the nut.
Also looks like a standard Jackson/Charvel trussrod cover should replace that one and fill the gap. Or you could remove it completely.