The spring loaded bulb contacts are "retained" in a plastic insulator. That insulator and it's contacts are retained into the lamp housing socket ID (rear protrusion) with a bayonet lock.

Your "bulb sleeve", I call socket.

I don't remember how the spring loaded bulb contacts are "held" into the insulator. I think they just float in there until a bulb is placed. So put a bulb in the socket after you install the bayonet insulator. I believe you can gently pull back on the wires on the contacts to "seat" contacts down in the insulator while installing bulb if you need to. Then everything is tight. Then slide the sleeving with boot down the wire bundle and onto socket OD (rear protrusion). You can slightly heat the boot or use soap. Needs to fit tight.

There is another bayonet for the bulb, as you know.

Test it to see it light before final install.

If you need to talk more, post good pics of all the pieces so we can be on the same page with names of parts and assembly.

Right is right, even if everyone is against it, and wrong is wrong, even if everyone is for it. - William Penn