I'd guess that you've a lower voltage running through the headlights for a dimmed effect when your on side lights. The spot light relay being sensative enough to pick up on this.
You could try taking a feed from the back of the stalk? A multimeter is going to be the only easy way to see where you can get a clean feed from.
Try taking a volatage reading from the fuse for the main beam with the lights in various positions (pull the fuese to the spots when you do this). That might be the best place to get a feed from thinking about it, since it's fused there shouldn't be any cross over to the other circuits. Or, if you know which relay operates the main beam, borrow the feed from this to trigger your spot relay.