I think that gets us closer to the right way of thinking about it. Somehow existence and consciousness are the same "thing", or two opposing aspects of the same "thing", where "thing" stands for something for which we cannot have a word, because it's beyond (or previous to) the distinction between object and subject. I think using the word "being" instead of "existence" makes things a bit more clear. Beings are almost by definition conscious. A stone (or a thermostat) is not a being, but an animal is.