You could try this with a hex-headed bolt, but the head might have to be ground down so thin that a socket wrench might not be able to grip it properly.
Now, Larry, pay attention: note how thin the original head of the blind-headed bolts are? You'll now have to modify the screw head and grind it down to approximately the same thickness as the blind-headed bolt in order to allow the taillight to seat correctly in the bucket. Don't forget to read your shop manual/electrical assembly manual and look at the diagrams showing how the wires are routed through the end panel of the trunk and connect to the wiring loom inside of the trunk. You'l also want to get some flat washers that will spread out the load from the screw head as it is tightened down. Then you will need to go to your hardware store and get some J-nuts that can be clipped to the brackets and corresponding flat-headed screws that have the same diameter at the shank as the bolts do. You can use a high-speed cut-off wheel to whittle away at the edges of the bolts, which look like flattened discs inside the taillight bucket, in order to remove enough material for the bolt to drop out and let you pull the bucket out.
It requires you to cut away/grind off the heads of the bolts so that the bracket will drop away from the bucket. There is a way to remove and reinstall the bucket without dropping the bumper. The bucket and bracket assembly was installed in the "Q" and then the bumper was assembled before being bolted to the body. The blind-headed bolts have a square shank beneath the head that goes through a corresponding square hole in the bucket to keep the bolt from spinning when the attaching nut is installed. Second, the '62-3 taillight bucket uses blind-headed bolts that go through the bucket and a separate bracket that holds the bucket to the rear bumper "Q".