Relay chatter from dimming dome lights

Hello, I am not too knowledgeable in electrical components but like to do things myself. Looking for some help here. 2018 Subaru WRX I installed LED lights (Opt-7 AURA LEDs) in the footwells and I want them to turn on when 1) the parking lights are on and when 2) the dome lights are on. A problem I have is that with my dome lights, they dim on and dim off causing the relay to chatter while dimming. With the help of an old topic (https://www.the12volt.com/installbay/forum_posts.asp?tid=131153) I drew up a diagram that should resolve the chatter. I'm hoping if you can check it: Question 1: Am I using the correct diodes 1N4004, 400v, 1A? Question 2: Am I using the correct capacitor 1000uF, 25v? If so, is it in the right place and do I connect the long and or the short end of the cap to the positive? Question 3: Will this even stop the chatter from the dimming dome lights? Thank you for your help. No need to read on but this is why I want to wire it this way. I want the footwell lights to turn on while I'm driving at night (which is why I want them on with the parking lights) and I want the lights to turn on as I'm getting in/out of the car (which is why I want them on with the dome lights).

All is good with the diagram. The negative side of the capacitor will be marked. It will eliminate the chatter.

Nice, thank you.