I wouldn't put him in the position of having to say no and feeling guilty (if I'm reading your interactions correctly). I'd just simply leave him alone in those situations.
If you really cant tell, just ask, with no guilt tripping, and with no emotion or expectation behind it. "Hey, that looks like an interesting project. Mind if I join you for an hour or would you prefer to work alone right now?" and then accept his answer.
I like this idea, especially if you can work out a good way to phrase it so he doesn't have to say the word "no". You could say something like "Are you up for a chat now or would you rather wait until [after dinner, after you finish the project, after the little one is asleep, whatever is applicable]?" Or even, "Hey, I'll be [place] doing [thing], when you get in the mood to chat come let me know." I don't know if that would help or not, but personally I like to phrase questions in a way that lets the other person communicate "no" without saying the word-it just seems to be less guilt trip inducing or pushy, IMHO for what it's worth.
Also, I just wanted to comment about use of the word "tired". I have read a good description of introverts versus extroverts as the difference in how a person gets energy. An extrovert gets energy from being around people and gets tired when alone. An introvert is the opposite, and gets energy from being alone while being around other people causes tiredness. This does not necessarily have anything to do with how enjoyable the person finds the experience of being around people or a certain person. It's about where the energy comes from.
The reason I say that is because to an introvert, to say "I am tired" really does mean in many cases "I need alone time to recharge my batteries, nothing personal." It doesn't necessarily mean "I am tired and need to lie down or go to sleep". So if he is playing a computer game or cleaning a gun or whatever, that doesn't necessarily mean he's "not too tired" to do those things but "too tired" to interact with you-it could mean that he's "too tired" to be around any people and just being alone is making him not as tired.
Having said that, it does seem to be a problem to me that he seems to react as though this is your fault. Hopefully this is a thing where you can keep communicating and it will come around to it really being nobody's "fault", nobody is "right" or "wrong", it's just a communication difference that you can resolve, so you both can understand each other's communication of love for each other.