I'd go for a 7-to-4 adapter as the pin out convention on the 7-pin connector is much more consistent since it's used by vehicle and RV OEMs. That isn't the case, unfortunately, with the 6-pin connector where trailer brake and battery charge wires are frequently interchanged on the pin-outs - this manifests itself as locked trailer brakes when one attempts to pull out after hitching up. The problem is so prevalent that there are 7-to-6 adapters that have toggle switches to swap these wires internally!
I believe the "missing wire" in the 6-pin connector is the auxiliary center pin in the 7-pin Pollak connector that's normally used for back-up lights.
Rusty