Hi all, I would appreciate some help with my question in the title. I have an existing switch in a bedroom that controls the ceiling fan/light. I removed the switch and found 1 wire that I'm sure is hot. This wire has been reduced from 3 wires, not sure if that matters or not. Along with this, I found another wire all itself that I'm not sure wether it's hot or not. Im guessing it is since the switch is there to stop or allow current when on or off, but i dont know a alot about this and thats why I'm here. These were both attached to the switch I removed. There is also a bundle of 3 wires that were all taped together in there, that I'm guessing are neutral. My question is how do I wire a new light fixture maybe 2 feet above this switch within the same wall cavity? I have plaster walls, and the wiring is wrapped in cotton sheathing that is very brittle. 15amp circuit, NY state, idk what else is relevant here, thanks to anyone who reads this or can help me out.

I thought my wife was nutz. First, she complained that a table lamp that she keeps next to her side of the bed wasn't working right and then, after I replaced the switch, she complained that the bulb was too hot. Of course, she always complains about these things at 2AM. "Go back to sleep, honey, I'll fix it in the morning." So the next morning, I take out my super-duper calibrated RayTek IR thermometer and point it at the bulb at a distance of 6". It says 350F. WOW! That really is hot for a 40 watt bulb. I take the bulb out and put it in a different lamp. The bulb reads 250 degrees and it is not as bright. Put it in a different lamp and it reads 180. I try a different name brand bulb and get pretty much the same results. So what gives? Why would one fixture be so much different than another (other than age.) And how do I get a fixture to be less than 350, which I think everyone will agree is way too hot for a 40 watt bulb? Speculation is welcome, because that is all I have.