Automatically hide and show the dock is greyed out, how to reactivate the option

To make the Dock instantly leap back into view when it’s needed, rather than slide, open a Terminal window and type the following:

defaults write com.apple.dock autohide-time-modifier -int 0;killall Dock

I find this useful, but if you’d like the animation for the dock to reappear to last for a split-second, try the following:

defaults write com.apple.dock autohide-time-modifier -float 0.15;killall Dock

To explain, changing "0.15" with any number can let you tailor things as it represents the time in seconds taken for the dock to reappear fully.

To revert back to the default sliding effect, open a Terminal window and type the following:

defaults delete com.apple.dock autohide-time-modifier;killall Dock

You could make it very small by pulling on the divider that is located to the right, usually just before the trash (a line) and it will turn in to double arrow when you click on it.