I've thought about it a bit more and it seems to me that the subconscious must store temporal information. Otherwise, how could I answer somebody who asked me how long I had been doing something if I hadn't specifically thought about time in the process of doing it? We must have some clock that runs separately from our conscious mind. But what are its properties?
This must have been studied in real experiments at some point, so if anybody has any links, they would be much appreciated. However, let me pose the following thought experiment. Let's say I'm put in a room with two light bulbs. While I'm sitting in the room, the light bulbs will both go on at some undetermined times. The question I will be asked after the experiment is done is, "After the first bulb went on, how long was it until the second one went on?" The experimenter gives me some sort of menial task to perform while I'm sitting in the room so that I'm unable to consciously count intervals of time.
Now I'd be curious of the actual results of such an experiment, but let's see if I can approximate the results from my everyday experience. First, what's the shortest time interval between which I can possibly give an accurate answer? That must be the integration time of our eyes, which is about a 30th of a second. Any less and I won't be able to distinguish the events. But is my brain good at distinguishing between a 30th of a second and a 10th of a second? If done in succession, I suspect the answer might be yes, but if you're just asked the length of time of the interval without any other information, it's not clear that most people could give an accurate answer. Can we distinguish between a 10th of a second and a second? I would say almost certainly, so our mind must have temporal resolution of at least a fraction of a second.
Unfortunately, this raises many other questions. Is memory of vision the primary means by which we store temporal information? Would a blind person be as accurate as a seeing person? Would we be as accurate if we were given auditory signals instead...with eyes open or shut? Do we use the outside world as our clock or is there an internal one? Our senses are our only links to the outside world, so if the answer is the former, then temporal information must be linked to our senses. I suspect that outside information must play a role, otherwise it would be a strange coincidence that the time intervals we can distinguish visually are comparable with those we can distinguish mentally.
What about long periods of time? If they waited a minute, an hour, or a day to turn on the lights, how would my accuracy change? It's hard for me to distinguish 59 seconds from 60 seconds, yet I can easily distinguish 1 from 2. The same would apply to hours or days. This implies that my temporal memory decays logarithmically. Is that because of an inaccuracy in my clock or a loss of information about the original event? Our memory clearly decays with time, so the latter must play a role.
The more I think about it, the more questions I get. I'd be very curious to see what a psychology expert has to say about these things.