The rectangular actuator looks to be Kohler P/N 1236014-CP (polished chrome). The expanded parts drawings show what looks to be common hardware for both part designs behind the faceplate; it should be a simple substitution.

Really !!!!

Curious to know if you tried this, and if it worked?

Howdy - yes, I replaced the shipped (phallic) faceplate with a more basic, rectangular alternative. The alt faceplate fit into the same opening nicely, but the mechcanical features for securing it in place are not aligned, so it is currently reliant on the semi press-fit coupling.. I am considering designing and 3D printing a coupling that will allow for magnetic attachment (tbd).

@livefromsf HI - would you mind taking a picture of your toilet? I am considering a wall mount to save space (I have a very tiny powder room). Also, thanks for the laugh on the phallic design!

I suggest the OP not consider installing a urinal either:

😂

@livefromsf are you happy w the veil? I’m considering it vs a toto AP but have been reading some negative reviews about low water in bowl and poop streaking! Pls lmk about tori experience! Merci

@kooks kooky I heard that the wall-hung design has a lower water level in-bowl, so I'd recommend checking out other designs (especially those with the motion-activated feature for pre-misting the inside of the bowl).

Thanks so much for your quick response response!! i think will go w the toto :)

@livesfromsf Hi - I just saw this and the picture is so helpful. Do you like how it functions?

I'm still working on my reno and want to do our powder room in a few months. My thought was to get a toilet like this to give me a bit more space in the bathroom!

@ kooks kooky which one did you pick? what is your experience? I am also leaning toward Toto but have been reading some negative reviews about low water in bowl and poop streaking!

@livefromsf did you find an actuator/ fix the rectangular one you used to replace the phallic one for your veil toilet - alas I have the phallic one and I hate it, especially when it is illuminated.

Hi Pamela, I hear you - been there! See my comments/response in-line above from ~2 years ago. This is the faceplate I used as a replacement: "K-8857-0 Bevel Flush Actuator Plate for 2 x 4 In-Wall Tank and Carrier System" https://www.wayfair.com/home-improvement/pdp/k-8857-cp-kohler-bevel-flush-actuator-plate-for-2-x-4-in-wall-tank-and-carrier-system-koh20943.html

Hi Pamela, I hear you / been there! Please see my comments in-line above from ~2 years ago. This is the faceplate I used as a replacement: "K-8857-0 Bevel Flush Actuator Plate for 2 x 4 In-Wall Tank and Carrier System" https://www.wayfair.com/home-improvement/pdp/k-8857-cp-kohler-bevel-flush-actuator-plate-for-2-x-4-in-wall-tank-and-carrier-system-koh20943.html