It may be that we have a problem in the interpretation of the ammonia test result here. We have seen cases where people were using CFL (compact fluorescent lighting - those thinner fluorescent tubes all curled up to fit in a regular lightbulb socket... or similar) that had a greenish cast to the light and it caused them to interpret something as 0.25ppm that others would have just called as yellow and therefor zero ppm. OR, in some cases people just call a darker yellow as 0.25ppm.
In any case, we do want to get suspicious if the ammonia makes a fairly substantial drop from 4 or 5ppm all the way down to some small or trace amount, like 0.25 or lower, and then just seems to stick there, as it could easily just be an interpretation problem.
Different bits of all the advice here are correct. Technically, in an Add & Wait fishless cycle you do indeed want to wait for ammonia to come all the way down to zero and then re-dose ammonia on the add-hour, thus sometimes producing the "pulsing" effect where the bacteria may see zero ammonia for some part of a day. But on the other hand, we don't want an incorrect interpretation of "what constitutes zero" to starve the bacteria for days.
One thing we can do in this particular case is to go ahead and re-dose and then observe how quickly the ammonia drops while its at the initial higher concentrations after dosing. The quicker that drop is, the more we'd be suspicious that the sticking at 0.25 is a bit of an anomaly. It could be that the testing tube wasn't completely clean from previous tests (a distilled water rinse can help with testtube cleaning.) Or it could just be light, as mentioned.
~~waterdrop~~