Using the automation mod, the "end day" button ends the day and shows the resulting stat changes (also kicks in log if there are non-stat-change events). Then you just click on start day (same button, new name) when you are done looking at the results of the previous day.
I think you interpreted the issue more correctly than me. I was thrown off by the part about not being able to sleep, and assumed that he is unable to use the START D. button.
So, just to clarify and expand your most likely correct answer. This is how it is intended to work:
And the reason for disabling the button was for the mod to have full awerness of when player ends or starts a day (to secure that the mod version of the log is correctly refreshed and when to begin automatic blowjob).
But, looking back at it now, I'm fairly sure that I could easily enough make the mod discover when a day has started or ended, without replacing the original buttons. It would also remove the risk of accidentally ending the day due to momentary brain farts.
I will most likely rework this, when I eventually get back to completing the mod.