I don't know as much as I'd like to. It's not a lie detector tool as much as a tool to flag things to look deeper into and question further.
Some of the things that stand out to me:
She seemed very bothered by the question of what happened, she was going to up and leave after that question.
She's eulogizing Lucas "your brothers and sisters miss you"
She's storytelling. Lots of um's and er's, lots of pauses. She gives too much info about the pull up, it's said in storytelling mode. That could suggest she wants us to believe it was the middle of the afternoon but it really wasn't.
She wants us to know that it's a 'fact' that she took a shower that Saturday. Is that the only 'fact' you've told us during the entire interview? Why is it so important to state that the shower is a 'fact'?
She has some kind of issue referring to JH by name or by his relationship with her, instead she's seeing him in terms of his relationship to the children "their dad". It could be because the children were on her mind during the relating of this part, or I think it's worth conjecturing that it might be guilt-related (feelings of guilt). What could cause feelings of guilt related to his status as 'dad', maybe that she's taken one of his children away from him and broken that relationship of him being dad? Or maybe it's about relationship issues between EG and JH.
What was said about he "could" have fallen during cooking dinner. Very odd. Is she inadvertently telling us that something did happen during cooking dinner the previous night? Let's not forget that she has child endangerment charges for 4-6pm the previous day...dinnertime?