before we start - do you have nitrates????
if no, then you must wait before the ammonia reaches zero.
if yes and nitrates are detected, then your tank is cycled
To answer your question......
In an Un-cycled/Non-cycled tank, it is unusual for nitrites to go to 0 before ammonia
BUT, in a fully cycled tank - it is extremely common !!
The main reason for detecting ammonia in a fully cycled tank and having zero nitrite, is because the tank has reached the limit/saturation for ammonia and cannot support the "ammonia" bioload.
Remember:
the good bacteria for ammonia and nitrite are DIFFERENT, and have different requirements.
The nitrite level is NOT an indication of the ammonia level (this is why both MUST be tested)
Hence, its possible to have zero nitrite, and have detectable amounts of ammonia in a fully cycled tank
To fix this.....
I would try increasing aeration to maximum - add lots of airstones to increase the oxygen (good bacteria needs oxygen to grow - especially the good bacteria for removing ammonia)
If this is a fishless cycle, I would stop adding ammonia and wait to see if the level decreases with the extra oxygen.
good luck