engine lights on 1990 BMW 535i

engine inspections lights - how do I check and clear. this is car i just bought and it has two insp. lights showing. Rear taillight pops on screen each time I drive.

I've checked and found the rear right passenger tail light intermittedly comes on and off. Is this just a loose wire?

I've also had a cracked oil pan (since replaced) is there supposed to be a protection plate to prevent such occurances?

Asked by for the 1990 BMW 535i
I have had this problem and had it checked. The repair facility cleaned the connection surfaces where they contact the bulb and the problem was resolved. I have had to do this periodically since.