Ive done connection work like what fairfax1000 suggested and if you do get the connection open and the old wire out, clean the connector so it will make solid connection to the new wire. I too would probably solder it afterwards but not a deal killer.
You could drill out the rivet or grind off the head to get things apart and then clean the spot where the hole it as to where later when a new ring terminal is riveted on, you get a good electrical connection.
You might also want to test things after things get fixed as the dual filament bulb requires a good ground and sometimes the crimped barrel connection to the hole in the stamped housing becomes corroded and not allow electrical flow but may be tight mechanically.
This is on my 68 Nova but the barrel of the light socket is crimped over to the light housing and if this connection is not there electrically then the lights will not be properly grounded.
Another option might just be to put a connection under one of the threaded mounting studs using an internally toothed ring terminal with a new wire that then on the other end gets terminated with a toothed ring terminal and grounded to where the original light was grounded at.
Jim