I think there’s some confusion here. He didn’t say anything about whether he’d take rebirth again. He just said that he didn’t know if the institution of the Dalai Lama would continue. He said that would depend on the wishes of the Tibetan people when the time comes.

Anyone who isn’t Buddha takes rebirth when they die. So if he isn’t Buddha (he says himself he is not enlightened) then he will take rebirth, but his next rebirth won’t be recognized as the Dalai Lama and could be anywhere.

As for Buddhas, it depends. Buddha Shakyamuni said he wouldn’t take rebirth again and when asked what happens to him after he dies wouldn’t answer. These are four of the unanswered questions in the Pali Canon:

1. The Tathagata (a perfectly enlightened being) exists after death.
2. The Tathagata does not exist after death.
3. The Tathagata both exists and does not exist after death.
4. The Tathagata neither exists nor does not exist after death.whether

In all the traditions then Buddha Shakyamuni doesn’t take rebirth after he dies but enters paranirvana - whatever that means.

He has however blessed the world by his presence. You can connect with him - through the sutras, and through the teachings and meditation, the inspiration of enlightenment and experience the teachings directly yourself. It’s like there’s no distance of time or space between you and his teachings (I think this is a Mahayana way of looking at it, not sure).

But in the Tibetan traditions you also have emanations of Buddha - so not of Shakyamuni Buddha, the historical Buddha, because he entered paranirvana. But other Buddhas can manifest in our world in many forms - as animals, birds, and even the likes of rivers, bridges etc. Or as a stream of rebirths of one person after another.

So, depends on whether you see the Dalai Lama as an ordinary person, as a bodhisattva, or as a Buddha. According to some of the traditions of Buddhism, it’s possible to see anyone as a Buddha, it’s something intrinsic to us all, our “Buddha nature”. So then it’s not so clear cut - the answer to the question, is someone Buddha or not? Because we all are, if we could only see it. And the other way around, according to the sutras, the first person the historical Buddha met after his enlightenment didn’t recognize him as Buddha, but turned another way, so couldn’t be said to have met a Buddha even though he met his physical form.

So as an ordinary person or a Bodhisattva he has to take rebirth in some form. As a Buddha he can emanate in many different forms even simultaneously, or can continue as a stream of Buddhas one after another, or he can enter paranirvana similarly to the Buddha. It seems to be a matter of choice in a way - but it’s also a matter of the wishes of the people and beings they are connected to.

According to the Pali sutras, then before he died, Shakyamuni Buddha hinted to Ananda that if asked, he could remain until the end of this world system. I don’t know what that means but Ananda missed the chance to ask him to remain, and by the time he got the hint, it was too late, the process of paranirvana was already underway.

So, whatever that means exactly, it seems to suggest that whether Buddhas remain or pass into paranirvana is not just a choice they make, but a matter of a combination of their connections with us, and the wishes and requests of those connected to them.

If nobody has the right connection for them to remain, they just can’t do it, because their physical body is a result of that connection with us, due to their past connections with us before they became enlightened, and our present connection with them (or something, I forget the details here), and without the connection from our side, well it’s like Buddha is right in front of us but we can’t see him or her.

This is subtle stuff so I’ve probably got some of this wrong, and it’s partly summarizing things I was taught long ago and don’t remember too well, but it may give a rough idea, enough to get started. Anyway it means that if you see the Dalai Lama as already enlightened, it’s much the same really as if you see him as an ordinary person or a bodhisattva still on the path - if the institution of the Dalai Lama no longer continues when he dies, still, if he is Buddha, he can emanate in many forms and it doesn’t stop that. It would just mean he doesn’t emanate as the Dalai Lama. His stream of blessings of the awkened mind could continue as a bridge, stream, flower, or new human beings, but not identified as the Dalai Lama.