Auxiliary battery harness question

[B_derK20]

On this diagram (from another forum member) are the two batteries connected on the positive sides or is the aux battery totally independent of the primary? The diesel K20 I once had just had a cable linking the positive terminals but this gas motor truck is either missing that cable or it wasn't that way from GM. Can I run a cable like the diesel trucks or will that defeat the purpose of the wiring harness that's already there?

Thanks