Hmmm, seems Mitsubishi have actually done something sensible - the wiring for halogen and HID is, as far as this exercise is concerned, the same.
So, for high beam, power flows through the relay to Fuse 3 and then via the Light Green wire to the left headlight. Power for switching of a relay to control a light bar or driving lights can be picked up anywhere from the fuse to the headlight. Possibly the best solution is an Add-a-fuse unit connected to Fuse 3 in the engine compartment fuse box. Best to take care to connect to the upstream side so no additional load goes through the original fuse, even if the current drawn by a relay is minimal. Do not use this fuse/circuit to power the ancillary light(s) - just the relay.
Connection of the rest of the light bar harness should be fairly simple, noting that some of those harnesses are set up for negative switching on Toyotas and may need appropriate changes to suit the positive switching of the triton.