tapping into amp power and ground

When I was redoing the interior of my car, I ran all of the amp wires to the back of the vehicle - power, ground, remote on.  After getting everything back together, I realized that I wanted to run LED lights, too.  I'd rather not try to run additional wires back there now, I know I can use a relay to power both the amp and the lights but it it a bad idea to use the amp power wire to power the relay, too?  Obviously I'd have to tie into it with a smaller wire (running 4 gauge).  If it matters, the amp I'm going to be powering is going to be 300-400 watts max. 

4g can safely carry up to 150a @ 12v (up to ~1200wRMS worth of amplifier power) -depending on how long the run is. So, since you'll only be powering a "300-400 watts max" amplifier, I'll say that your 4g will be fine to power a relay for your lights.2013 Kia Rio -90a alternator

DDX470HD GTO14001 GTO1014D (x3)

Big3 in 1/0G

1/0G to GTO14001