No they don't. If the dealer follows the install instructions, they only come on with the headlights. The kit itself has a relay that only sends power when headlights are on.
I followed the honda instructions and my fogs come on with the parking lights so long as the button for fogs is pushed in. I think it may have something to do with the relay and plugs that are used.
This is a big secret I guess. Every single thread about this has zero info, just people saying they've done it. What's the big deal? I'm just too lazy but I could easily figure it out by studying the wire diagrams. I'm sure it's a simple tap the the parking light wire from somewhere. Impulse did it too but he won't say how.
No, I did not tap any wires. I just used the wiring and plugs that came with my kit (it's not OEM Honda fogs). That might be the thing - I bought OEM STYLE foglights, so they are set to turn on with the parking lights.
All I know is that my fogs will turn on/off when the parking lights, driving lights, and/or high beams are on.
The instructions that were included with the foglights were not thorough. I had to use the Honda instructions in order to install them (I think that's why my wiring was too short...). The wiring of the fogs goes under the steering column into the fuse box. What I know from that is that the power to fogs is actuated by the headlight switch.
This is a big secret I guess. Every single thread about this has zero info, just people saying they've done it. What's the big deal? I'm just too lazy but I could easily figure it out by studying the wire diagrams. I'm sure it's a simple tap the the parking light wire from somewhere. Impulse did it too but he won't say how.
I luv what he siad, he starts off like he's gonna help you but then he contributes to not helping anyone... lol
not hating, just thought it was kinda funny i guess but yea, im trying to find it out as well, i have it right now to where i can turn it off even if the car is off, so it really doesnt matter if the car is on lights on or off.... but im trying to figure it out. when someone does find it out and is willing to let us know... TELL US!!
i'm guessing the dealer i took it to followed the directions i linked you too... i don't know why they'd put instructions on how to install it with the headlights only but then bother to make it so they come on with the parking lights also.
The link above will take you to some VERY good instructions on how to do this mod to an RSX. I did this over 3 years ago, the mod never failed, never gave me any BS. Except the brights indicator didnt work, but I got use to it, but then got fed up and figured that out myself later...
Anyway, if someone would like to see if the wiring is the same on the civic's, this migh be a good guide to start. I could be wrong, but I bet they are similar if not the same. I just havent had time to get in there and look...
but yea, im trying to find it out as well, i have it right now to where i can turn it off even if the car is off, so it really doesnt matter if the car is on lights on or off.... but im trying to figure it out. when someone does find it out and is willing to let us know... TELL US!! 
i don't know why they'd put instructions on how to install it with the headlights only but then bother to make it so they come on with the parking lights also.
