I said don't trust pen testers, but ironically in this instance it was telling you the live earth wire was live!Like I said in original post I did my P16th papers (20 odd years ago like) so not up to date but yes replacing 2 core to 3 core no problem but I’ve no issues not using the light switch on the wall and just the pull cord.
When I was testing the wires one the earths was showing live and someone comments don’t trust pen testers!
I’m able to do whatever I just don’t know where to put which wires - one of the earths is scorched so maybe that’s the live one!
It needs to be established if there is a permanent live at the pull cord that is not coming from the wall switch.