Not sure if it's the same mechanics of a late '60s emblem, but I don't think they changed the workings much over the years. The emblem mounts to the backing plate via a post in the upper left. I don't believe it would be riveted, you wouldn't be able to replace the emblem without buying an entire assembly. The post is inserted through the backing plate and is secured with a spring pressed behind the plate and attached to the post that holds it snug. The spring is fastened and twisted to apply the turning pressure to return the badge to the down position. If the spring is weak, the emblem will flop beyond the stop. The opposite would be true; If you flip the badge open to unlock the trunk and it doesn't stay against the crescent stop, you know the spring is definitely too weak. If the spring is in good condition you may be able to simply reinstall it with more tension.
I thought I had an old one apart to show you, but couldn't find it. The two pics here show 1) the badge in the up position against the crescent shaped stop 2) looking from above while badge is in the same open condition to show the stop on the backing plate (arrows). That stop sits in the space behind the badge and then rests under the crown to hold it in proper position. It is all dependent on the spring load of the emblem mounting to the backing plate. Replacing the spring is a pretty easy fix, but when removing the lock mechanism you'll be glad it's a Cadillac sized trunk! Hop in and get comfy!!
