Coil burning up

If the engine's not running than the coil is seeing solid 12 volts instead of a "pulsing" 12 volts from the pickup unit ... normally the engine is running and the coil sees a brief negative signal that completes the 12 volt circuit Why would anyone leave the key on if the engines not running ? Why not the ACC?

In desperate need of help No acc. I was being towed so turned it to on position to put it in neutral within five minutes smoke rolled from the coil. It's the third coil