you can do what AFRLme said with action parts "show/hide interface". This will show/hide not an individual interface, but an interfaceclass.
So set you closed inventory as "secondary interface" or whatever category is still available (it is possible to create new categories with the exploer ctrl+e) and your open inventory as "inventory".
Assign both interfaces to your character.
On the closed inventory add an action area. Add an action to this action area, either when clicking or entering the area (whatever you like best) and execute the action part "show interface", select the open inventory. And "hide interface" and select the closed inventory.
The opened inventory needs to have an interface area and then add an action on leaving that area (found in the properties tab of the interface) where you hide the open inventory and show the closed one.
And of course you would need to hide the opened inventory at the start of the game. So add the "hide inventory" action part (with the opened inventory selected) in the start action (game properties)