You don't need a continuous amount of ammonia, as long as there is some in there. That's how fishless cycling works. You add in pure ammonia and dose it back up to 4 ppm every time it gets below 1 ppm. That way is quicker and safer, and you can fully stock your tank as soon as it's finished. Also it requires only one water change, right before adding fish. The only negative is that your tank is empty for a month or so.
Also, the bacteria used in the nitrogen cycle can live for a month or so without food, and pretty much only live on surfaces, not so much in the water. Just some info.
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