We need to define Existence to answer this question, and as I have noted in other posts we need to understand a little history to understand what it means. The key is to understand that Existence is different than Being. Being is unique to Indo-european languages, which Greek is. So Greek philosophy grew up in a worldview already embedded in Being. But then with the Arab conquest of the Greeco-Roman world, the language shifted from Greek to Arabic, and Arabic did not have Being, but rather Wajud, which means “that which is found”, which is basically a kind of existence. So the Arabs as they mastered Greek Philosophy came to understand that the Greeks were talking about something they did not have in their language, so they split Being into Wajud (the existential substrate) and Kun (which means to Make) was used as a technical word for the rest of Being. Then when these arab texts were translated back into Latin, the Italians had to make up a word to substitute for wajud, and they created the word existence with the same range of meanings, which was what is found when there is no projection, and also ecstasy. So now that we know what Existence is we can approach your question.
We definitely exist if we are found, beneath the projections of Being. Existence is like the rock beside the road that no one cares about and so it sets there untouched because it is not valued by anyone, that rock has existence, but it does not have the kinds of projections on it as a piece of gold or a diamonds. So to the extent that no one is projecting on you you exist, and the cumulative projections on you are related to Being. These projections tend to be illusions and delusions, and are what you are calling “someone else’s thoughts”. Thus we exist to the extent we are found beyond all projections, and then an overlay on top of that is the projections that are maintained by the thoughts of others, which is from the point of view of Existence illusions because they do not exist in the same way that things exist that are found.