All of this was explored in more detail in part on of Last Yagami Standing. Now here's the proof from the narrative.
Our first sighting of Sachiko Yagami, in the Death Note manga, comes as Light returns home after finding the shinigami notebook. This supposedly verbose lady hears his key in the front door and calls out, "Light, is that you?" Then hurries out to intercept him. Not saying a word, just standing there smiling. In fact the kanji in the background reads 'smile, smile'; her aspect glowing out in anticipation and pride.
And Sachiko lets him
This isn't how she usually greets her son after school. She's not generally rushing to intercept him with unspoken expectations of information about his progress.
We see that in later panels, when Light returns home from an ordinary school day with no examination results in it.
Then it's all a warm welcome home, called through from the settee, where Sachiko is enjoying a nice sit down, reading her magazine in her spotless home. Enjoying a lovely cup of tea. I think.
What is going on in Sachiko Yagami's lap there? I can't work out if she's stroking a strangely pointed nosed puppy (or cat), or else holding a tea-towel beneath a white cup in her hand. Or polishing something. Knitting? Either way, she doesn't get up.
Though peeping around the bannister at the foot of the stairs is a common position for Sachiko to be standing, during interactions with her son. She ends her first scene there and returns to the spot for her second.
Here we see Mother Yagami's qualities as a human alarm clock. Not trusting her son to keep an eye on the time himself, she calls up when it's 6.25pm, thus he has to be leaving for cram school.
Which is a bit of a good job, as Light was busy serial killing at the time, thus not at all watching the clock.
Still no fuss, and certainly none of that aforementioned 'verbosity'. Just a simple heads up and she's gone again. A mother doing her best by her boy, but not in some pressure driven 'soccer mum' way.
She doesn't need to. Light's more than enough pressure on himself, having already informed Ryuk that he 'has' to be the best, hence studying, cram school and all that, undertaken of his own volition.
So there's Sachiko - quietly supportive, not pushy and certainly not babbling.