John, I had similar problem in an old GTO....center electrode and spring of the lighter socket had broken off the base. When the lighter was removed the center post droped into and contacted the socket body, a direct short to -neg (ground) which popped the fuse. But when the lighter was inserted (and fuse then replaced) it held the center post in position and worked intill the post and spring worked free and fell into the socket again.
It's a simple fix...Replace the lighter socket. Avilable at most chain auto parts stores and resto-part supply houses....Jb
Even with the key turned off the lighter socket will still be hot. As long as the contact isn't shorted, sure leave it in, That is, as long as your Ipod charger doesn't burn up. I have always been told not to run a power supply without a load attached. Many opinions on this though