Aha! That was the magic setting I was missing. I enabled the TimeCorrection, and although it didn't have to correct time, since all logs where correct all the time... It works now!
So to be clear, when it said unpause, it was the 00:01 task as task #1.
Now that I added the second task at 11:59 with pausedownload, it says
"Mon Apr 01 2019 00:44:12 Scheduler: pausing download"
edit: And when I turn them around, it also says the same pausing download message after reload.
To be honest I never got this one working over several updates. So what happens is that NZBGet perfectly manages to Pause the downloads on a certain time. But it never manager to unpause it. I've tried different times. Putting the task behind the pause, before the pause. It just doesn't work. I see ...