My ST 7.5 also came without the 2 extra terminals. Those terminals were connected to additional turns on the main windings to provide 220V at 50 HZ - at the 1500 RPM needed for 50HZ, the generator doesn't produce enough voltage, so extra turns were provided. In the US market, no one needs 50HZ, so they saved money by not including them.
Between the two center terminals there should be 2 links stacked together (it may look like one link at first). Remove the two links and put one to each of the two outer terminals, and you'll have rewired the head for parallel operation, or 120V only. That should eliminate the hum from the unbalanced load created by only using one side of the windings, but leaves you without 240V. There are ways of digging into the internals and re-wiring it for 240V that won't hum, but it's not a quick easy mod.
The idiot light and switch don't do much - mine was wired to the 120V output (I think), not the harmonic winding.
You can either replace the doghouse or wait until it falls apart and then replace it; when you do, it's not too hard to create a receptacle on the generator side with all four wires and two different plugs to match with it - one that puts the windings in series for 240V and one that puts them in parallel for 120V only. Don't change it while the generator is running!
If you leave it wired for 240V, normally the center terminals (where the links currently are) are used as the neutral, or white wire. Electricity doesn't care what color the wire is, but following the standard will be helpful in the long run.