I would put light on only one prim. That's because avatars can see only about four point lights at a time-- so if four avies with nuclear face lights are present, chances are no one will see the point light on your lamp. So one will be better than two.
And yes, setting the point light on a prim will not illuminate it. It will make it a source of light. Objects around it will be lit on their facing sides. It must be dark, or nearly so, though. Light is pretty much undetectable at noon.
Full bright makes your prim LOOK as if it has lit up. So if you turn your bulb bright full bright when it's touched, it will provide immediate feedback (at dusk, dawn, or twilight) that the light is turned on. Same for turning the lamp off.
If the bulb is to be your point of light, it will cast light on the shade, but it might be best to make the shade the lifght emitter.
With point light you can specify:
color
intensity (how far the light effect can be seen)
radius (now far it's seen)
falloff (how fast the light fades as distance from the emitting prim increases.
If you play with all this, changing the lamp state (full bright bulb and point light from on to off), via llSetPrimitiveParams), I think you'll get it.