How to set STFT-parameters to visualize woodpecker / Sawtooth Signal? ​
Your first problem is that you have your axes mixed up.

Your "17 Hz" picture shows this quite clearly.  The red bars are the impulses from the signal.  The bars should indicate an impulse (wide range of frequencies) but your axes indicate they are across time.

This is what it should look like:


Notice that the bars are along the frequency axis rather than time as in yours.

This is your woodpecker recording:



It contains bars, too.  But, they are not as wide band and are much closer (in intensity) to the background noise.

The bars repeat at just above 20Hz - you can see that the frequency is around 23Hz in your last plot (the red line plot below the blue oscilloscope style plot.)

Your overlap of 0.95 amounts to a time resolution of about  just about 40Hz.  You need a higher overlap of maybe 0.99 to separate the bars.

You could downsample the recording down to like 11025 Hz sampling rate.  That would get you better frequency resolution and make calculating the spectrogram faster.  You can do that because there's not really much of interest in your signal above about 4500Hz.