Ok, sorry, you'd just be surprised how many people think they didn't come with one simply because they just never payed attention.
I've never heard that you could special order a MKIII without a security system. I'm going to have to look into that further. If anything I suspect that's just something the dealer offered as the is no p/n for a wiring harness without provisions for the various components, nor are any of them flagged as options in the EPC from Toyota.
If the head lights come on but don't rise when you install the dome fuse a short across either the feed for the headlight relay coil or across both HL fuses is a possibility (the relay's more likely).
If they pop up and turn on then it's either a short across the green wire with the red stripe which runs from the switch to pin #3 of the Integration Relay #2 or the line which used to run from the Integration Relay #2 from the former stock security system (yellow with a blue stripe).
Of course there are other possibilities, I'm just trying to point you in the direction of the most likely candidates.