What goes into the "mystery jug" (small plastic jug with screw on cap by the firewall on passenger side)? What does it do? It is in an 87 base model 5 speed if it makes a difference.

 

It's the sub zero assist reservoir, assuming you are talking about the squareish reservoir made from white plastic between the shock tower and firewall.

You can remove it, and cap the vacuum port on the manifold. Mazda issued a TSB years ago to remove this pointless system.