DMT is produced in your body, and your, brain, all the time. Regardless of the state of wakefulness. This is something that has been tested clinically. It would not be able to cross the blood brain barrier if it were not for the fact that your brain actively transports it across. MAOI destroys it extremely quickly, just like it does to serotonin and other chemicals, in order to regulate a constant level.
So, you are always experiencing the effects of DMT. Just like you are always experiencing the effects of serotonin. And just as the levels of various neurotransmitters - and efficiency of transmission - are in a state of flux over time, so the nature of our consciousness also fluctuates. Accounting for clinical depression, schizophrenia etc.
As to the endogenous dump of DMT from the pineal at times of stress such as death, it hasn't been proven or dis-proven. The theory didn't emerge from nowhere for no reason. Since no person has actually come back from full necrotic brain death, our anecdotes are still influenced by our tether to conditions of what we call life. It is entirely possible that the DMT dump is not a sudden release, but has preconditioned kinetics which enables the transition to DMT space to fully occur after the point in death when we are completely dissociated from all familiar forms of state-specific memory.
About DMT during sleep: again we have no data as yet to show that there is increased DMT in the brain after crossing the liminal threshold of sleep. The nature of in vivo testing makes this difficult. However it is a sound working hypothesis of an ever growing sector of the scientific community. It may be that during sleep we simply produce higher levels of DMT, but since a whole array of other neurochemical systems alter during sleep as well, it is another subjective experience altogether.
In vivo, all such things are hard to corroborate and reproduce as empirical evidence. But this doesn't mean it should not be taken seriously and studied further. Such has always been the nature of psychedelic research in psychiatry in general. And we will be soon mapping the brain with psychedelics, to produce the best model of the mechanics of mind we have ever had.