Why did relay run when I applied half the nominal coil voltage?
The simple answer is this:  It is guaranteed to switch with 12v on the coil.  It is guaranteed to not switch with 0v on the coil.  Between those two voltages, there are no guarantees about what happens.

Or, to put it a different way:  0v=Off, 12v=On.  Somewhere between 0v and 12v it must switch between off and on.  It's not like it will stay off from 0v to 11.999999v and then switch on at only exactly 12.0v.  Some relays might switch on at 4v.  Some at 6v.  Some at 8v.  You might even buy a bunch of the exact same relay and some will switch on at only 4v, while others of the same relay might need 8v to switch on.  But you know that it will be off at 0v, and on at 12v!

Just to confuse matters, there is the voltage at which a relay switches, and a different voltage at which it will stay on.  For example, if you slowly raise the voltage the relay might turn on at 6v.  But if you then reduce the voltage, the relay might not turn back off until it drops below 4v.  6v would be the switching voltage, but 4v is the holding voltage.  

Of course the switching voltage and the holding voltage will vary from relay to relay and are not usually specified in the datasheet.  Of course, with Radio Shack you almost never get good datasheets anyway and this is no exception.