Reason for bimodal behavior while low second fourier coefficient
Two peaks does not imply a frequency of 2 - for example the peaks could be very narrow and/or their spacing could corresponding to a much smaller interval than half the time-series length.

There is no information about the overall shape of the time-series that can be drawn from the knowledge of the second DFT coefficient.

I have plotted here 15 time series (left) and the magnitude of their FFT (right). 5 unimodal, 5 bimodal, and 5 trimodal series.