Reconnection is of course a pseudo-pedagogical concept. There are no physical "line" to snap, or reconnect. Also, all magnetic fields are solenoidal, having no beginning or end. So the concept of snapping or reconnecting is more or less incorrect. It's all about the underlying current structure. When the underlying current structure changes, the magnetic field lines are instantly redrawn. The lines only indicate relative strength and direction at a given discreet instant. The next instant they are completely redrawn to depict the new state of the fields at that moment. However it is a fallacy to regard the field lines as reified 3D objects of their own capable of twisting, coiling, snapping, etc. The fields may store energy, double layers may store energy, currents may change and the magnetic field lines get redrawn. But snapping magnetic field lines simply doesn't PHYSICALLY happen. In reality there would be not one but infinitely many field lines, all in constant flux. That single lines are used is a convention. Spacing denotes strength of the field, not an abundance or dearth of field lines themselves. They're only a visual aid.

One wonders if there are double layers in the magntotail that are storing energy and then releasing it when they break down?

Much of the stuff, as you say, it probably in space. However, currents in space can induce currents on/in the ground as well.