Got the same/similar problem here! IS200 Sport - 2001.
Parked the car yesterday, only to be told later I'd left the lights on... you all know the rest ;)
My light relay was making a hell of a noise, so replaced that today in the hope. But no, problem still persists and I'm £60 down already (Lexus Poole).
With the ignition ON, and lights turned on - they work OK and the relay (old or new) is quiet and normal. If I select "Auto" the lights just dim up and down, and after a few seconds the relay starts buzzing away. Same if I select "Off" too!
With the ignision OFF, it doesn't matter what I select for the lights - they come on after 2-10 seconds.
So at the moment I have the relay out, to ensure the lights stay off.
I haven't had the windscreen replaced. There is no water in the fuse/relay box, bone dry and clean in there. Haven't checked the one in the drivers footwell yet though ???
Will check there tonight, but having spend out on 4 new tyres this week and I dont fancy a new fusebox too! Doh!