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.