Billy - If people do not understand the question it will be because it was unclear.
1) The transformer will require four connections - two for incoming power and two for the 12 Volt output.
2) Transformers do not (ever) require an earth connection - it's not like on a car - forget car electrics.
3) You talk of a blue "core" presumably you mean a blue wire
4) If you can't see connection #4 then you're not looking hard enough - you MUST have four connections.
5) If you use Google and select IMAGES and enter KTB 105 Transformer you can see pictures of it
6) The mains input will either be a single hole with connections inside or two visible terminal posts with screws.
7) Have you taken the lid from the transformer to look inside?
8) If the blue wire is attached to the secondary of the transformer then that will be one of two wires for the 12V output. You will need another wire.
9) The colour of the wire is immaterial - any colour will do.
Good Luck...
September 2016