You can splice pretty easily without taps.
Use an exacto knife to peel a 1/2" of insulation off the source, open up a bit of the wire strands inside, strip a 1/2-3/4" of the wire you're attaching (before you do, slide a peice of shrink tubing up so you can slide it down later) and separate the strands a bit as well.
Stick some of the strands though and wrap everything around each other. Then seal up with shrink tubing (slice down the side to allow you to wrap it over the wire). A couple dabs of liquid electrical tape and you're sealed up.
If you don't feel like doing that and want a 3 way splice, go to a hardware store and buy a few sizes. My guess would be 14-16ga. Take back what you don't need or just keep them for possible use later.