Both Harry and Jesse are autistic. Harry wasn’t officially diagnosed until he was an adult, but he’d self-diagnosed long before that. Harry made sure Jesse got a diagnosis as soon as she started showing autistic traits, and ensured that she got any and all accommodations that she needed throughout school and college. He didn’t want her to have to deal with any of the problems that he’d faced before he had an official diagnosis.
They’re both very prone to hyperfocusing on projects- Jesse’s “ten-year-old determination”, Harry’s fixation on defeating Zoom, etc.
Because they both do it, it’s really obvious to them when the other is in hyperfocus mode. It’s become automatic for them to accommodate for that, and make sure the other is eating properly and remembering to sleep.
Harry has trouble with empathy and noticing other people’s emotions, whereas Jesse tends more towards being hyper-empathetic.
They both have quite black and white concepts of morality, but in different and often clashing ways. Harry is very “ends justify the means”, but to Jesse morally wrong behaviour is never excusable. That’s why she had so much trouble reconciling “my dad is a good man” with “my dad murdered someone” and ended up running away. Harry, on the other hand, couldn’t understand why she had a problem with his actions because to his mind killing Turtle was entirely justifiable because it was to protect someone he cared about. They’ve been working on understanding each other for a long time, but this is one area where things are still really difficult for them.
Jesse communicates a lot with her face by using exaggerated facial expressions to add extra meaning to what she’s saying. She’s always done it, and Harry is very grateful because it means he can read her a lot more easily than he can read other people.
Routine and familiarity are important to Jesse, and they provide a lot of comfort. It’s why she was so desperate to get her old life back after being Zoom’s prisoner, and why she found it so hard to adapt to life on Earth-1.
Harry is very blunt, and doesn’t always pick up on things like metaphors and rhetorical questions. Jesse is much better at that sort of thing, but not always. She’s spent a lot of time explaining slang terms to her dad, and has developed some subtle signals to let him know when he’s missing things.
Harry mostly stims with his hands, fidgeting with pretty much everything, but he also does things like spin in chairs. Jesse is more of a pressure stimmer, hence her preference for more fitted clothing.
Harry’s baseball cap is a sensory thing as well as an attempt at a disguise. He likes the feel of wearing it, and it also helps cut down on bright lights which bother him a lot. Jesse has similar problems with brights lights, and they get worse after spending so long in a dark cell. They keep the lights in their room quite low for both their sakes.
They both have special interests in the sciences, and will info-dump for hours about anything they find interesting. When they both get going at the same time it’s nearly impossible for anyone else to get a word in edgeways.
Jesse cycles through special interests quite quickly, whereas Harry tends to retain them for a long time. They share interests a lot, and also tend to pick up things from each other due to their mutual love of info-dumping. Harry know so much about Disney princesses, you would not believe, and tiny Jesse alarmed more than one teacher by displaying an in-depth knowledge of violent action movies.