The points should be firmly mounted as the coil is. The armature is the inner shaft that moves inside the electromagnet.
It looks like yours are missing the nuts & locknuts that open the points. Check this cut away. It looks similar to yours but has a different projecter cone.
http://navyaviation.tpub.com/14329/F...-Horn-311.html
Here is a GM type but there are similarities with all vibrator types.
https://www.hometownbuick.com/1952-buick-signal-system/