There needs to be a source of ammonia for the bacteria to feed on in order for the cycle to complete. It should never stay at 0 ppm for very long. You may have just starved off your first order of bacteria. There are two types of bacteria that complete a cycle, as you may or may not know. First order coverts ammonia to nitrite, then the second order will then convert the nitrites to the least harmful nitrates. I suspect there's a little bit of ammonia in your tank that can't be detected or else there would be no increase in nitrite levels. I would at least add some fish pellets to the tank and check ammonia readings every few days to make sure the bacteria has plenty to eat. Otherwise, your cycle will keep crashing. An ammonia source will need to be added until fish are added. You can and should use pure ammonia if you can. Just make sure it's pure and have no scents or surfactants in it (foams when shaken).
So what is a good level of ammonia to cycle with? Depends on who you ask. Some like to build the colony of bacteria quickly by adding 4-5 ppm of ammonia, while others use 1-2 ppm. A majority of tanks would do fine with the latter dosing. Reason being is there is no need to establish a huge colony of bacteria that can consume 4 ppm of ammonia in 24 hours if you're just stocking a small school of tetras and a few otos. There's just no way that the bioload would ever produce levels this high, so the majority of bacteria starve. However, if you're adding fish that have huge bioloads, the high level of ammonia to cycle would be recommended.