I have a 60 year old ranch home. Everything was fine until a couple of weeks ago. My daughters ceiling light and a wall outlet, both wall-switch operated, do not work at times. But I found if they don't work, and I go to the next room and turn on the bathroom light, this outlet and ceiling light will come on! I believe the wiring for these rooms is right above them in the attic and there is a junction box up there that these outlets/switches might share. Why would they intermittently not work unless the bathroom light is switched on??

 

It sounds like you have an open neutral wire. When the neutral is open..... changing loads can cause different parts of the circuit to "appear" working. Although you see a light come on... there is not full power available.

You are going to need a voltmeter to check and effectively find out where the problem lies.

The other alternative is to find out everything on that circuit and then check at each location for a loose connection. Look for wiring that is just pushed into the back of a switch or receptacle. You are looking for an issue in the white side of the circuit.

 

PJ is certainly on the right track with his idea for the cause of your problems. Another possible way to check it would be to power the circuit off and check each location for resistance between ground and neutral. It should be 0 or awful close to it. If it's open or extremely high resistance you're at or near the source of the problem. More than likely you have a loose neutral connection in one of the boxes, if somehow I work at cut within the walls this is going to be a major issue to track down.

 

You may have a bad splice or connection at the other switch. It is common for the wiring to be daisy-chained. A bad connection can affect portions downstream.