Based on that drawing, 4 wire, and since A: engine start works, B: alternator charges the house batteries, C: shore power/ gen set doesn't charge the chassis battery and none of the wires from the B.I.R.D match whats on the isolation relay; the wire between the B.I.R.D and the engine start switch is missing/gone astray. If that turns out to be the case this will be the second missing wire and I begin to wonder how many others are not there/or where they should be.