What does a high pitched noise that comes from a wall indicate?

If it's a mechanical noise check the chimney stack (from ground level of course) and see if there is a spinning chimney 'granny' on the pot.They can squeal when they turn in the wind. Also, chimneys that have been closed off must be ventilated to avoid condensation forming within the chimney and the inner walls. There may be a vent in the wall near the lowest level of the chimney and the 'capped' chimney pot will allow air flow. In windy weather you can get noise. These things will not however cause a constant noise at an even level. If it IS an electrical hum, perhaps it would be an idea to ask the neighbour to listen to it and give her opinion. Once she is involved she is likely to be inclined to want to solve the mystery and you might be able to persuade her to switch off her electrical mains switch for a moment or two and you will know for sure whether the problem lies with a piece of electrical equipment in her home. In that case, I am sure that she will want to locate the source and end your misery.