It should be a DC voltage so set the multimeter to DC Volts (start on the 200V scale - it won't be anywhere near this value at all but it is always safer to start high and then lower the scale to get a more accurate measure) and then connect the meter between an earth point on the motherboard and one of the pins.
Be careful not to "bridge" the meter's test probe across two pins and short them out as you may damage something.
Here’s an image from a different laptop that shows what I mean. (sorry that it is a bit small)
Even though it is a 40 pin connector the principle is the same. LED power (VDD LED) is always there on pins 1, 2 & 3 whilst the backlight on (BKLTON) lead is connected to pin 4.
Again this schematic is not the one for your laptop. It is only to show how it might be wired, so the pin connections might not be the same. It is unfortunate that you can’t find the make and model number of the panel to get the datasheet to make it easier. Did you try searching for the motherboard schematics using the motherboard’s board number at all?
(click on image to enlarge for better viewing)
If there is no constant LED power on any of the pins as you say there is a problem with the LED power supply on the motherboard.
If there is LED power available then it may be a problem with the backlight on circuit, either on the motherboard or in the panel or the LED power circuit in the panel.
That is of course if it is wired like this and I don’t know if it is or not.