For example, it is not clear from the literature whether any genes are actually expressed during interphase II, and if there are, whether any have specific functions during that period.
In the mouse, transcription appears to be suppressed during meiotic maturation (see here and here).
There is evidence (see here) that protein synthesis is required for exit from interphase II, but this is likely to be due to the need to synthesize new cyclins, following their degradation after metaphase I.
As you note, some organisms have essentially deleted interphase II altogether.
