Just been having a look at wiring diagrams - dont have the one for yours but using previous one, and a bit of educated guessing.
What I think is going on here is this:
The main beam is ignition dependant (i.i it is on only if the ignition is on.) These feed of a central power point (i.e. the ignition switch). Off this point runs the headlights, radio(the control side) - the amp will run off the fixed on power due to load(they havetwo power supplies to avoid overloading the circuit), the wipers, the indicators etc.
The side lights are not ignition dependant (i.e. work all the time).
I think the eatch point on one (or both) front wings is connecting all the wires (e.g. side light, indicator, dipped beam) together but not putting it onto the wing (likly some corosion between contact and wing).
This is then causing power to run through the sidelights, through the earth into the earth side of the dipped beam bulb, out of the live side, back through the switch, to power the wipers control circuit (at around 6 volts) and then back to the wipers earth, reducing the radio down to 6volts as well.
Ill have another think as this does not explain all the symptoms and i'm not fully there with a fully diagnosis yet....
What would also help is for you to remove the sidelight bulbs and the diped beam bulbs from the circuit on one side, and then the other to see if it removes the fault as I am sure this is an earth problem. - Would also be interested to see what happens when you put the indicators on with the side lights on (do the side lights come brighter and the indicators dim or vice versa)
The other thing to check is that the wing is still electricaly connected the the rest of the landy - if all the bolts are shot you could be losing voltage here as well.
I'll try and find a 300tdi circuit and put my mine to it over the next few days and let you know.