I always wanted my fog lights to be on all the time when running but the only mod I saw was to have them on when the lows and highs were on . I wanted the fogs to act as running lights and be on as soon as the car was started .I know in Canada that's the way they came but for us in the USA it was not the case.
This how I did it .
Find the fog light relay in the amongst the fuses and remove it .

I found ignition power at empty fuse location #16 , "heated seats ",
which is not used in the 318is .

I made a jumper wire out of some wire and spade connectors.

I connected the wire from the two locations .


Finished look .

Results

If you were worried about fusing this you could solder or connect a fusible link into the line .