Ammonia going up towards the end of fishless cycling.?

What is your pH and KH?

Your pH is crashing due the KH being used up in nitrification. If you tap water is higher KH (at least KH 3), then do a partial water change to restore some buffering to the tank. If the tap water is low KH as well, add sodium bicarbonate (also known as bicarbonate of soda and Baking Soda) the standard Arm & Hammer stuff from the grocery store.

You want to have some buffering and have the pH and KH a bit higher. There is nothing wrong with pH 6.4, but the KH of zero is dangerous, and even at 6.4 you are below the optimum range for nitrification bacteria - good catch, I'm glad you posted before it got worse.

I don't know the size of the tank, but 1/2 teaspoon (measuring spoon, level) per 50 gallons should raise the KH about 1 degree. the pH will rise with the KH. Don't bring it up more than a degree at a time if you can avoid it (tricky in a small tank, easier the larger the tank). Once you have started adding bicarb, you can wait 12-24 hours and and more to get the KH up where you have more margin for safety. Shoot for a final KH of ~3 degrees (or about 50 ppm, whichever scale your KH test uses).

HTH

That should help a lot. Nitrification uses up KH, and fishless cycling at the normal high ammonia level uses up a lot - which allows the tank to drift toward acid, out of the optimum for the bacteria. That is why your ammonia reappeared, the bacteria for that were not as healthy and vigorous as they had been when the pH was higher. It would really slow down the whole process, and if it really crashed (pH <<6), it can damage or even kill the developing bacteria.

But your water is buffered enough that you can keep it under control with partials, which is great.