Besides what others have mentioned, I don't see the purpose of tying this into your high beams. High beams are legal for public road use. LED light bars are not.
If you tapped off the high beam supply and still added a switch to control the LED light bar so it can still be kept off when high beams are on for road use, this does not seem to have any advantage over wiring independent of the headlights, would be about as much work too once you have to splice into that.
It has the disadvantage that we have no way of knowing how much current the Multi-Function Switch can handle. In brand new condition it is just acceptable for headlights, but as it ages (or replaced with a generic Chinese one) the copper contacts corrode, grease hardens, internal resistance rises, so if you do wire to the headlight circuit anyway, then I would at least open your MFS and clean the contacts or else you may melt it from the additional current.
At only 4.3 amps, you are still within a comfortable margin where you don't necessarily even need a relay (to just wire it direct, not through the MFS). You could run battery positive-fuse(immediately after battery)-light bar-ground return wire to cabin where a switch is in series with a good chassis ground. This leaves your existing wiring 100% stock. Just make sure to pick a switch that is rated for plenty of DC current. DC needs more robust contacts to survive arching.
Odds are that your light bar has a buck switching circuit inside of it, so itself is not very sensitive to voltage drop like an incan bulb is, but for mechanical fortitude I'd still use at least 18ga or lower wire.
However, if this is a generic Chinese light bar, and you haven't measured the current yourself, it could be lower than what they claim. Often the generics use 3W, 5W, or even 10W LEDs, multiply the number of them to tell you a wattage, then divide that by 12V to tell you current, but the circuit usually doesn't run the LEDs at full power because the enclosure has insufficient heatsinking to handle that much heat, and because your higher 14.(n)V system with alternator operating, should result in lower current to the LED bar circuit than if it were at 12.0V.