The door handle plunger attaches to an actuator rod via a threaded shaft and a couple of nuts. I suspect that either the shaft has come loose of the nuts have fallen off.
You can see this clearly by going to the fiberfab assembly manual in the "library" section of this site (I would use the 1984-ish version) and find it on page IV-22, or you can look here:
https://www.speedsterowners.com...9537/FiberFabB-1.pdf
Regardless, you'll have to remove the door inner (trim) panel and then everything will become evident.