I’m no expert but what I deduced when looking into these for our Horsa project there are three patterns of cockpit lamp carrying that stores number all listed as a Mk.II lamp.

Pattern.1 – Metal – has a knurled edge and a raised centre to the top switch.
Pattern.2 – Metal – raised centre to the switch removed in favour of a flat top.
Pattern.3 – Bakelite – economy version with chunkier grip to on-off switch.

Pattern 3 was still in use up to the 60’s – seen them in Vulcan cockpits. Possibly the 5C/366 -> 5Cx/5162 re-designation is a post-war re-organising of things?