The reason for your problem can be found in the lower lefthand area of this wiring diagram .

The foglight relay's coil gets it's ground through the high beams filaments when the low beams are on . When the high beams are on the relay's coil has +12 volts on both sides and the coil obviously won't engage . This is how GM wired it so that the foglights will work with the low beams only . What's happening is that your LEDs aren't at all happy being connected as a ground source for your foglight relay's coil .

Were this my problem to solve , if I wanted to keep the LEDs and have functional foglights , here's what I'd do ;

I'd cut the light green wire at the foglight relay at terminal "C2" leaving a few good inches of wire on the relay side of the cut wire , and I'd ground the cut wire leading from the relay , and then tape off (insulate) the other end of the wire from the harness (that was leading to the relay) . This way the LEDs will never see the relay's ground load and the foglight relay won't need the high beams for it's ground . Bonus points are that the fogs will now work in either low or high beam , which is how I personally like them to work (I've done the green wire modification on past cars even without the LED headlight problem simply because I don't like my fogs going off when the high beams go on) .

 

 

 

Your Welcome , I'm happy you had success with it .