I heard from the Walker chuck folks today.
The chuck has somewhat mysterious provenance. The block on the side must be a shop-made addition as is the square actuation drive.
Advice is to clean all the goo out of the inside but to not separate the magnetic pack due to the risk of injury and damage to the components.
I'm to add .25" of 90w gear oil to the base and seal it up with Loctite 77.
I'll have to either make a handle or re-make the square drive because it's a wobble-fest now.
One minor question...how do I measure a hole to size a roll pin?