NavList:

It's for a small lightbulb in the index arm that lights up the arc.

The 'cable' should be plugged into one of the two sockets in the metal disc at the top of the handle. The other socket is for the optional bubble horizon attachment.

(It's not really a cable, just a wire. The electrical return path is through the frame of the sextant)

The handle is a battery compartment. Unscrew the knurled black disc at the bottom of the handle, insert two AA positive side first.

There is a small black momentary switch towards the top of the handle. The lamp in the index arm should light up when you hold it down. Interestingly (?) on my C&P 'Bobby Schenk' the button is on the other side of the handle - under the thumb instead of under the index finger.

There's a ridged grip pattern on the plastic part of the index arm that is right next to the 'Horizon' plaque. You can carefully slide that part towards the plaque to expose the lamp. Notice how there is a bit of exposed copper wire in the housing that connects to the socket of the lamp.

I'm describing all these bits because all of them have failed in one way or another over the years. For example right now there's a bad contact in the wire and I'll have to replace it.

Replacement bulbs: I think they are Lilliput Edison Screw (E5), not sure though. Maybe search NavList first.
https://en.wikipedia.org/wiki/Edison_screw#Fittings

Hope that helps,

Luc