1963 Jaguar mute assembly
This thing goes in there and then something rocks on this and something is underneath, too.
The foam part of the mute, which actually the whole thing is all about (no muting without it), is missing. Mouse-pad foam or black self-adhesive weatherstripping is a common replacement, and there should be the “official” replacement part (from the MIA reissues) available.
Up to now the picture showed the spring assemply orientated in a wrong way. As can be seen on Mel’s tech page, the screw depresses on the metal part and the spring pushes from below, not as it was hitherto shown in my picture with the screw penetrating the spring.
Many thanks to John Holmes and Kirk Kopetsky for the hint.