Never played the game, but behavior can be pretty specifically made for certain scenarios. Drawing the lines is not really that hard though. An entities' position is basically represented with a vector (x, y, z position in space) and you can simply draw a line between the 2 positions.
As for the behavior itself, I don't really know what you want to do, but if you for example want the characters to not be able to move a certain distance from each other, you can simply do (position1 - position2) and check for the distance.
I think it would be wise to look into vector and matrix math and you will figure certain things out you might want to do.
move the *control points* of the bezier curve around a bit using a periodic function such as sin() or cos() ( because the values of sin and cos range from -1 to 1, the lines will move both up and down). Try that and check if it works. You might be in for some heavy tweaking though
One alternative (and more complex) way to achieve that effect is to use Inverse Kinematics on the line connecting the character's finger to the back of the puppet.
Looks like maybe a string simulator, although somewhat tricky since the "target length" of the string is constantly changing to keep it pulled fairly tight between the two characters, but loose enough to boing up and down nicely. I think it should work just fine, to change the stretch constant for a string every frame (not so constant now, are you? )