2006 Honda Odyssey
when I shift my car into either PRND there’s a chance that the dash light won’t light up for it.

so if I shift into D, the light may come on, but if I go from D to R the R light may not come on.

the car itself will go in reverse, but the car won’t know it’s in reverse?

the real issue is when I put it in P
the car will stop and act like it’s in P, but when I turn it off the key won’t be able to turn all the way off because the car doesn’t know it’s in P. So I get into a situation where I can’t take out the key, or start the car until I over ride the shifter to go swap between P and R until the P light comes on and I’m able to take the key out.
usually only takes a try or two.

can anyone tell me please what part may be responsible for this?

this can happen for any mode, not just P
sometimes the RND lights also won’t show and I’ll have to shift to another gear and back again for it to light up