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The Strategy Guide States:

Italy will normally enter the war in the spring of 1940. However, Allied movements could bring this date forward.

 If any of Gibraltar, Malta, Cairo, Tunis or Damascus are abandoned then in every turn in which this is the case, Italy can
move 1-2% towards the Axis, and British or French National Morale will fall by 500, depending on who owns the empty
location.

My question is once Italy is "At War" does the "Empty Location" penalty no longer exist?

I don't believe so - no. Once Italy is mobilised there is no penalty for leaving those areas unoccupied.

there is penalty in french morale, (in Europe) if you abandoned the french units outside Europe, if you want thouse french units, take the tunis unit only. its a risk,,but dont take two units, because a disaster morale happened worst than flank Maginot

The National Morale penalties only apply when Italy is neutral. Leaving them empty once Italy has joined the Axis is at your own risk!