When you're dealing with light, things mix in an additive way. If you keep adding different coloured paint, everything goes brown. Keep adding different coloured lights, you'll eventually end up with white.
Often with pixel art you'll have a primary light source and a secondary, or ambient source. A good example is an outdoor scene on a sunny day, with rocks. Rock surfaces pointing at the sun will be lit with white or yellowish highlights. The ambient light is blue (from the sky) so add some lesser blue highlights to areas of shadow. See Owlboy as an example:
https://i.guim.co.uk/img/media/65ddfa576ec0d5ba823cb8ab88383b829fc35c89/35_67_1064_639/master/1064.png?width=1920&quality=85&auto=format&fit=max&s=1ee98609b41e6e66bc4d3edb3ca52ac1The theory is that without the direct light from the sun, everything would be blueish from the ambient light. (Don't start talking about how there wouldn't be any ambient light without the sun. Just don't.) The sun with its whiteish light gives us the natural shades from the rock. The ambient light is coloured and changes the hue.
This could work in other situations. Imagine a cave with lava (or orange walls) and a lit torch. Again the torch would give a direct yellowish/white light. The ambient light would be red/dark orange.
On a street, you might want to use some of the tarmac or pavement colours as ambient light, or reflected light from any large nearby surfaces.
Then there are other light sources. This should be obvious. If your object is in the way of something emitting green light (like an LED display or neon sign or something) then mix in some green highlights where you think the light will hit. Take into account whether you think the light source has the ability to overpower the main source of light in the image.
I don't know what you want to achieve with the palette. I'd have to see the context of the object you want to draw. Right now I'm not sure I understand your question properly.