I think you are seeing my EbNaut transmission using 0.5s symbols.    The transmission itself is a little under 6 minutes long, and repeats every 10 minutes, so there is a 4 minute period of unmodulated carrier every 10 minutes.   .

That appears to be roughly what your grabber plots are showing.  The energy is spread over 2Hz while it is keying, so in a narrow bandwidth FFT would appear to reduce in power

The frequency of my transmission is very accurate.  Overnight the DOCXO output, divided down to 1Hz, shifted, on average over the entire 10 hour period, just 2us compared with GPS.   That corresponds to a mean frequency accuracy of the 10Mhz reference of 6*10^-11  - which is pretty good for a free running source..   It will shift a bit more when the central heating ramps the house up to 20C starting from 0600.