It's a big thing because to him, going down the assessment route on its own might be like pinning a label on him he may not be comfortable with sidling up to. He might feel like there is something 'wrong' with him. I say this because having raised one child with autism, my youngest, it's very clear to me that my middle child is on the spectrum. She's 14 and her school's psychologist said to me, for the first time a couple of weeks ago, that she's beginning to realise that DD may actually be displaying signs of autism. I've often thought about this over the years, and I've been fairly certain that DD is on the spectrum. But I've had to tread very carefully. Some children are ok with being assessed. Others may feel a bit 'persecuted'. When I tried to approach the possibility of assessment, DD did not respond well. That was a couple of years ago.
So just know the lay of your son's land, emotionally, before you broach the topic of assessment. It's bigger than we realise (especially for older children). From ages 10-13, it takes so little for children to feel 'othered'. Those are tender years. We feel so exposed to the world at that age.
Recently my DD did say, "Sometimes I wonder if I am on the spectrum. But I don't really want a diagnosis because I'm sort of just comfortable with the way things are. I don't want to get too deep into it and start identifying as autistic." She may change her mind. I don't want to push her. So this is her. But her friend, on the other hand, was totally liberated by her diagnosis at the age of 13. It was life changing, life affirming! She finally felt comfortable in her own skin.
So it lands differently for each child. Just, take some time to prepare your son and talk about it together. It's a big thing.
All that said, having had the experience of raising one diagnosed child helps me parent better, read the room better, understand the situation better, use language more accurately, wisely, and with care. I take care of how I approach him... and people in general. Your son's research of Simpsons jokes (which has led him to analyse and question what it is that makes them funny- I really like this!) is very much the mindset of my youngest; an analytical, contemplative, questioner of life, which I love. My youngest happens to love The Simpsons because of the jokes! Our two would probably have really good playground talks about their opposing views, yet similar interest (for different reasons) in The Simpsons. My son's 10 too!
I think assessments are great because they can give parents and other people in the sphere insight into a child's behaviour that may have seemed nebulous, leaving the child to be misunderstood. Assessments help us create our own map of our child's inner workings. Also, great understanding, empathy, and patience as a parent. I know when to push, when to pull, and when to stop. I know the lines I cannot cross. You really start seeing the world through a sensory lens and it changes things. I was so scared, years ago, when my son received his diagnosis and all of the unknowns that came with that. All I could do was love a mother's love. How his autism would manifest itself wasn't for me to know or have control over. Scary... and calming, all at once. Having a child with autism has made me an exceedingly patient person. And I know how and when to ask for more support and input for my son at school.
A diagnosis gives you more leeway and more volume when you need to ask for that additional support. It is certainly helpful. I would pursue it for sure, if your son is ok with it. I hope your son will be comfortable. I know that with autism comes anxiety and a bit of hyper-fixation. So, hopefully, assessing him won't encourage that anxiety. Best of luck to you. It's a bit of a long pathway but worth it if you can get on it.