I have a 94 Honda Accord and I am having problems with the parking light on the right side everytime it rains they come on whether the car is running or not and if u are driving it and it is raining and they come on the right turn signal wont work and when u shut the car off they stay on

 

Thats interesting. I imagine a short in a relay from water entering wherever that is. I'm not entirely sure. Id suggest an FSM or haynes manual, locate any relay or fuse associated with the light and then track where water would enter.
Thinking about my car (97) id imagine there is a leak that is getting into the cabin.

I have an FSM pdf for the 5th gen if you need.

 

My 95 does the same thing. Except it's not only when it rains, it does it whenever it feels like it. Only way to get it to turn off is to unhook the battery for a few seconds. Haven't been able to figure out why it does it.