Why is my kitchen ceiling light not turning on with the light switch?
Agreed that you need to verify the light is not working first by switching the light bulb with a known working light bulb. If that doesn't work is there another 3 way switch that is off now that you didn't know you had?
That was switched off by somebody else since you didn't know it existed.

Can this light only be turned on and off from the one location (i am trying to figure out if this is a single pole or 3 way light switch your testing.)

If its a single pole switch (only two screws with wires under them) than when you put your light up probe on the contacts on the switch it should light either full on or full off. (depending what position you have the switch in , up or down) So if its half on than something is going on.

If its a 3 way switch than maybe your putting the probe on the wrong contacts to get a full light. A three way switch has 3 wires under three different screws.

I am just trying to think out loud because I don't know what to think.

Maybe its a bad ballast (in a fluorescent light fixture) giving off funny voltages which I am not even sure makes sense. What kind of a light is it?

Maybe the neutral in the panel is loose (i know I have had half voltages on plugs when the neutral was loose in the panel even though I wasn't in the panel recently).

Let me know how it goes.