Nick
As a blow boatperson I do knots. The square or reef knot is considered one of the worst ways to join the ends of two lines. Under tension the knot will always pull out. I've been told the square knot has killed more men than any other knot. As a boy the first thing I was taught by my dad about knots was to use a bowline to join two lines.

I note that there may be a rope locker on a sailboat, but there's not one single piece of line that is called a "rope." Can't fathom why it's called learning the ropes when there aren't any. I've never found bungie or shock cord, as sailors call it, to hold knots very well. So I would vote with Grant's recommendation.

Additionally, I would stitch the wipping twine through the bodies of the shock code several times to sew the ends together. Shock cord is basically a bundle of long rubber bands held together by a woven nylon tube. So you'll need a heavy sail needle to get through it. A roping or sailmaker's palm is helpful too. A quarter in your palm will work to push the needle through in a pinch. Just be sure you've had your tetinous shot. Don't use pliers to pull the needle through the cord or you'll create nicks which will cut the material. I keep a 3-4" disk of inner tube rubber in my ditty bag to grasp the needle and pull it through heavy material.

I looked at the knot suggested by CLC. It's basically a double overhand knot. Normally you would stay away from the overhand because it is vey difficult to untie once it has been put under load. It may work on bungie but is going to make a very bulky knot. Additionally, you're going to have to leave tails of reasonable length to allow for initial slippage while the knot sets up tight.

Happy rope working sailor!
Geo. C.