There were some other UK users discussing this and some issues with the software as it worked with a tow bar on another UK thread - might be worth digging into that thread
My Invincible finally arrived a week ago (need to post thoughts on the UK page) and I have the flanged towbar option. The dealer fitted this and the electrics for £800. I’m sure you could get it done cheaper by a mobile fitter or your local mechanic but Dave had a nightmare with the electrics so I would only use the Toyota main dealer. They did try it on with the cost so watch out for that, they originally asked for £1,500.
I like that style of towbar as its height adjustable and very solid, a big lump of metal which suits the ruggedness of the car.
This all happened early on when Toyota UK hadn’t given the dealers the pricing for extras. I think £1500 was just a number they made up on the spot so I pointed out that the 2022 car’s towbar had cost £800 and I could get it done by a towbar specialist for less than that. They then said that the Hilux towbar was £800 so they would match that which seemed fair enough so we agreed on it.
Ask them (or get someone else to) what they are charging for Hilux towbars as it’s the same job on both cars. If that doesn’t help then just get a specialist to do it as £1500 to bolt on a towbar is truly ridiculous.