Damped sinusoidal form FFT of signal
What you have is a very sharp rectangular boxcar shaped function.  It is approximately centered at the mid point of your data set.  Your magnitude spectrum looks correct, in that it is a really low fundamentally frequency with a ton of harmonics.  Your FFT without ‘absolute values’ is presumably plotting just either the real or imaginary values.  The oscillation in that plot occurs because of where that pulse is centered in the data set.  It’s unlikely that plot has any useful information.  I have no idea what you are trying to find from this endevour, but if you were interested in the period of the pulse you could zero of the end of the data set, providing more granular frequency data that you could use to measure the fundamental.  That or you could just measure it directly, which is probably a lot easier.