Firstly, it does not sound physiological since he has no problems when crated though some might say a vet should check that out.
I do not know the layout of your home, but conceptually, I would start by gradually expanding his space. For example, maybe, maybe go from the crate to a pen. Then maybe from the pen into the room the pen was in, etc. At each stage of expansion I would make sure that he eats and has his bed in that available room/space as dogs do not like to go where they den.
One other thought, you have not defined whether "gone" is a #1 or a #2. If it is #1, it is possible that it is a submissive pee depending upon the hierarchy of your dogs and how they behave in your absence.
Hope these thoughts are of some help,
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