Can anyone help with my bathroom light pull chord switch?

[Avo Mk8]

Looking through all the pictures and posts if the switch outside the bathroom is not needed then just lose the brown / blue T&E at the pull switch and it then looks like you are left with a live, switch live and an earth from the light fitting position in the remaining T&E

Agreed. My reservation was the apparent (post #20) 4Kohm resistance between red & black in the (disconnected) run between the lights. Could be lots of things, including me misunderstanding what is said, but really an IR test would be prudent before connecting it all back up!