Adding Auto Unlock

The diode across the coil is normally put there to supress the big voltage spike that occurs when the relay switches off. Without it, if you have some electronics like a transistor controlling the relay, it could possibly cause damage by exceeding the maximum voltage. In this particular application, it prevents the relay from briefly switching on again if your 12V control signal happens to switch back to ground rather than an open circuit. Without the diode to bypass the coil, it might energize the coil in the reverse direction for an instant until the cap discharges. If your control signal just opens up when it switches off, you don't need the diode at all. You might want to be careful using this method depending on what you're planning on using for the switched line, because of the current that gets quickly discharged back through the diode from the rather large cap. Though this would work, I'd use a transistor for the timing control so you can use a much smaller cap for timing; 1000uF isn't as cheap or easy to get as a 1uF, and with a transistor driver, the timing won't be dependent on the particular relay you use.