No idea about your specific car, but in general, I believe they do.
Quite a few years back I started noticing, what I perceived as, a lot more people driving two footed and/or driving way too close to the car in front of them such that they had to constantly brake. While I’m sure that’s the case for some of them, I don’t think driving two footed (or otherwise riding the brakes) is nearly that common and I came to the conclusion that that it was their cruise control maintaining the distance.
We’ve covered this before, in fact, I even asked the same question about the same model car as you.
I can’t answer the OP’s question but my ex-wife’s RAV4, when holding down the “set” button which also decelerates the car (in most cars this is similar to taking your foot off the gas) would apply the brakes after a few seconds…or rather did something that actively slowed the car down. I assume it was the brakes. I remember being able to hear something that sounded pneumatic happening when it activated.
I think, but don’t remember, that the brake pedal actually moved down when CC applied the brakes, so the lights would have turned on regardless.
In any case, the easiest way to find out, and it’s how I checked to see if they come on in my EV when I use the paddles to slow down (they do), is to go out at night, set your cruise control and then use it to decelerate your car when someone is behind you. You should be able to see the brake lights reflect off of their car. Even without someone behind you, if it’s dark enough, you might be able to see a little bit of light from the high mounted brake light bleeding back into the cab.
You could check to make this method works by first just braking normally to make sure you’ll be able to see some type of reflection from them.