See, you're making the same mistake— an observer at the location of the water when? You want to say "now", but there is no such thing. Taking a picture doesn't help the issue— you only wind up tangling yourself up in it.

This stuff was all figured out in the first place through thought experiments, so let's try one to demonstrate what I mean. Let's say there are two real events we can talk about here. Someone at the reservoir poses, the light takes twelve billion years to get here, and we snap a photo. Then say there's a second event, the draining of the reservoir, which happens (at the reservoir) one year from the time the person poses.

What we want to know is, has that event happened yet, even though we observe there to be water? So on your suggestion, as soon as we take the picture, I jump on the spaceship with a copy and fly over there at near to the speed of light. Twelve billion years after they posed, the person at the reservoir will look up and see me lift off from Earth, and then very soon after I will arrive carrying the picture to ask them about. (Of course I'll already have seen the event I want to ask them about, but set that aside for now.)

Okay, so here's the fun part. While I'm travelling there, at very near to the speed of light, time stops for me, or very nearly. I perceive the journey to take a matter of hours, say. I arrive at the reservoir carrying a still-wet photograph to ask them about. They say, "Oh, yeah, that happened about twelve billion years ago— a year before we drained the reservoir, wasn't it?"

"Ah hah!" I exclaim. "I had a hunch the water was already gone when I left."

The reservoir people think I'm nuts. "We drained the reservoir almost twelve billion years ago. You only left Earth a couple of hours ago. Of course the water was gone."*

This is true. From my perspective, I have just taken a picture, flown for a couple of hours, and the reservoir has been gone for billions of years. But, no matter. Bearing my prize, a notarized letter affirming that the picture depicts events one year prior the draining of the reservoir, I hop back in my spaceship and make for Earth. Again, a journey of twelve billion lightyears seems to take a manner of hours. On arrival, I disembark, waving the letter triumphantly.

"See? We were right! The water was gone a mere year after we took the picture."

"We know," says Earth. "We saw it happen one year after you left."

"...I haven't been gone for a year," I say with a sinking feeling in my gut.

"You've been gone for twenty-four billion years. We watched you leave, and one year later the water was gone. A couple of hours ago we saw you arrive at the reservoir, get the notarized letter, and lift off again; now you're here."

"No, no," I protest. "You only think that just happened a couple of hours ago. It takes light twelve billion years to travel that far, it's ancient history by now. This letter is twelve billion years old."

Suddenly, it occurs to me that I am trying to argue that events that I personally witnessed a couple of hours ago are, in fact, ancient history. I am holding a still-drying photograph which Earth insists was taken twenty-four billion years ago, and they have twenty-four billion years of history to prove it; I am also holding a notarized letter which both I and the Earth have just seen signed mere hours ago, and saying that it is twelve billion years old. And yet I know that these objects are only hours apart in age.

I realize that if I flew back to the reservoir to get double-confirmation, hours later they would say that they had just seen me arguing with Earth, and they took my side, although according to their records the letter was actually notarized twenty-four billion years ago and not twelve as I had been claiming. I realize that no matter how many trips I make, I will never be able to make it so that I, the Earth, and the reservoir people agree about the order of events.

"You know," I mention to the Earth, "I could have saved a lot of time if I had just read the Wikipedia article on the Relativity of Simultaneity, couldn't I."

"Yeah, probably," the Earth says. "Sorry about all your friends and stuff."

* cf. "a frame of reference which agrees with the theoretical frame of reference of a spaceship we launch today, at the time it arrives at the reservoir"