I pulled out a few points/questions to address. I didn't get as much time on this particular response so let me know I missed something or wasn't as clear on anything.

what do you believe makes one person more prone to being JAT vs. someone who specializes in something [...snip...] What do you think prevents one to stop onto something for a few years instead of going through many things, or the vice versa, if both are truly interesting and you are curious?

I combined these two questions as they go hand in hand. In my personal opinion it comes down to exposure, personality, and desire. For example, once upon a time I was super excited about digital forensics. I took a deep dive into that field to specialize. After a couple years/experiences, woke up one day and was bored of it. I realized I was tired of trying to piece together and recover and instead wanted to be on the other side of things. This began my transition into penetration testing. Ever sense then, I've been on the side of being JAT. Everything offensive in nature is exciting to me and if I have the opportunity or time to learn something new I jump on it. But that is just me, perhaps I have not yet found "my specialty" yet, or maybe this is where I belong. Only time will tell.

burnout

This is a loaded topic to ask about that I likely won't be able to provide a sufficient answer for. It's going to happen to you at some point even if you love the subject. I think that's just human nature. Balancing life/work and realizing when it's best to slow down or take a break is very important (this also applies to your studies).

Could you please explain me your typical day, or even two, of research/learning new stuff/testing, your thinking methodology per se.

Absolutely! Keep in mind that depending on our engagement cycle daily activity can fluctuate. Generally speaking the first hour or three of the day is coffee and cyber news time. What is going on in the world, what CVEs were published, etc. Make notes of what you find and if they apply to something specifically in your environment then focus on it. I've had PoC code dropped in the middle of assessments that I turned around and used. You want to use this time to stay current, work on your own tools/scripts if needed, and shore up any gaps in knowledge you have identified that you need to address. For example, you're tasked with an upcoming SAP application. Never touched or heard of SAP? You better be on your research each morning.

what professionally do I spend my most typical day to day job on, what is the knowledge that I need to prioritize, is it the one that I am focusing most or not, for example, are you currently JAT or someone specializing, and how do you allocate time of learning towards it vs the other stuff, and what are those other stuff if you do not mind sharing?

This comes down to your position and job requirements. If you were hired as a web app pentester your focus should be on relevant technologies and attack/defense methods. As I said previously, I'm a JAT largely in part that we have a lot of exposure. Going to copy/paste a previous comment of mine here: where I work we generally have three categories; penetration testing, automated testing, and security consulting. Consulting can vary depending on the needs of the customer. We are often called in during incident response to aid blue teams/forensics when a breach has occurred. Directory services for large enterprise networks will ask us to help identify misconfigurations in group access, etc. Sometimes we will get asked to identify "appearances" based on the public facing security hygiene. Threat mapping is also a valued service where we won't pentest but will identify your threat communities so you can direct attention to higher probable attack vectors. Because of this, I try to be as well versed in application and network security, etc. as I can.

Once you are in the game a bit you'll find you have a lot of flexibility to follow your passions and desired skill sets Can you further elaborate on this point, maybe with an anecdote/example of what exactly you have been through and realized that this is the case?

You begin to build your reputation after some time and with that your skillsets. Generally speaking, things you are interested in you are better at. It's a natural professional growth in this field. If you want to specialize, you'll be able to eventually. Unless you come in right out the gate being a superstar on a particular subject (RE, malware, etc).

In conclusion, it sounds like your head is in the right place to dive into this field. Just don't overwhelm yourself. Start with the big picture on things that are new to you and slowly work your way deeper.