From my personal experience in a relationship with an INTJ, and my non-ENFP approach, and its results:
Yes, he thrives on tackling a challenge, with the motto that the process is efficient, and the result being something productive [he does NOT like "wasting" time - although, this sometimes, resorted to us debating on what would be considered "wasted time"]
When you've already got a plate full at work, and you're looking for a hobby to do aside from that, to have something *else* in your life...do you like it when someone at that point demands your attention...demands you to focus on them and deal with them? And I do mean that in a good way.
What has worked with my particular INTJ, is laying the cards on the table upfront, first. Meaning, making sure that they're indeed, at that time, "looking for a hobby to do aside from [work]". I never really go the route of, 'you may be saying that you do not need X, but you really do need X.' As such, I'll respect their wish for alone-time to focus, and leave 'em alone, and usually make their environment more condusive to be able to focus more greatly [e.g., them ranting about how many other shit they gotta get done, that's irritatingly on their to-do list, on their minds, and tackling those for them, so they can concentrate on their PROBLEM].
I also go the route of asking if they'd like to brainstorm with me. If they agree, then they throw out all they need to tackle, the limitations that's slowing them down, the frustrations, and I just question and question, from every angle, for them to see their PROBLEM out of their zone/tunnel vision. And for them to get a perspective on it, rather than circling around the issue, in the thick of it. And when the "EUREKA!" moment hits their eyes, I just ruffle the hair and say, "I have a feeling we're gonna celebrate soon." *wiggle my eyebrows and growl* And leave. Them to their space, time, to the idea, its motivation, before it slips away again.
Without fail, THEY seek me out (finally), and their enthusiam (towards me) is lovely and endearing and appreciated. And, that's usually when I like to harness their energy, creativity [I can use Ni for fun now! Woohoo!] and intensity that they're exuberantly wanting an outlet for, by making myself a challenge - and unlike the work stuff, it's a playful and fun challenge. Although, I don't go the bratty route; as, for me, deliberately being so makes me feel ingenuine and foolish. But, I do resist being immediately "tackled" by giving them a run for their money, one-upping playfully - which, come to think of it, can be seen as bratty, in a sense - but, I'd wager we (you and I) manifest this vastly differently.
Although, I understand that sometimes distraction is the best medicine, especially when I see that the stress seems to be crumbling them more and more, rather than leading to a resolution. However, they have to be receptive to the distraction - and that can only be gauged, case by case, situation by situation.
Do you like it if they challenge you to a mental fight, if you will, in which the rewards can be great, but you'd better work for it?
He loves it - but the timing is key. Otherwise, such a challenge is swiftly shut down and not appreciated.
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Also, if I'm feeling unappreciated, want attention or feeling taken for granted/ignored, I have always laid it out in the open with the INTJ. I do not like situations to build up - I'm very fast to confront inter-personal issues as soon as they appear [my issue is with tackling or discussing long-term issues, but particular incidences are handled swiftly, when it's fresh in both of our minds]. Starting off with how I perceive where they're coming from, how I read their action/reaction/inaction [giving that particular example(s)] and my thought-process that made me reach my feeling that I felt. Although, I have a tendency to state it as a detached observation. And, whether they can understand why I felt that way, and if not, what particular aspect of it they didn't understand or agree with or they think I erronously perceived. And, he does the same [although, it's not very easy for him to do so, compared to me, tackling particular instances/issues, but he's better at tackling the long-term stuff].
Plus, I have stated something similar, a few times, to the INTJ:
"Sometimes, you have needs that need to be respected, but it can happen at the same time that I have my needs, which are conflicting with yours. It's only natural that if one is always being the understanding one, the sacrificial one, such that one's need always overshadows the other's as more "real-world important", inevitably, resentment will follow. I don't want this to turn into a competition...er....conversation of whose need is more legit and why. I just wanna figure out how can we meet each other half way in such moments? What can I do...? What can you do...? What can WE do...?"
^ I save that shit for after, when they're not hassled with work-challenges, when they're relaxed (thus, receptive), to tackle the convo.
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If being a brat is your thing/way to flirt, then reading your particular INTJ, and the particular situation, and timing it such that brattiness is seen as frustratingly endearing and not a frustrating nuisance, would be key.