Looking for some advice - extending wires.

I need to extend a remote trigger for my bicycle horn. The trigger goes into the device with mini-jack. Pressing the button closes the circut making the device work (produce sound). Inside the cable there are two wires as shown on the photo. The red and gold. They should not touch each other as the circut will be permanently closed (and this should only happen when I press the button). Both wires red/gold feel metal and inside the there is material like core (white). I got couple of the triggers hoping that I just remove the button and the mini jack and extend the trigger that will be used on the bicycle. The way they are inside of the casing the both wires touch each other yet the circut is not closed which only happens when I press the button. I connected the red with red and gold with gold from two separate triggers and it does not work. So the wire that carries the current myst be inside - perhaps the fabric like (the white on the photo) is the one. Any DIY friendly way to do this ? I think my idea of connecting the wires and wrapping it with electrical tape will not work. Or where could I bring it to have it done for me by a professional. It has to be water tight too.