if what he said could be true, how can it be a logical fallacy? it's just a theory. if he said it must be true without question, then maybe it's a fallacy. i dont know why, people like to run around calling everything a fallacy, but then again i shouldn't expect otherwise on a debate website. if a cave man thought maybe things could travel faster than light... he's not committing a fallacy, he's just speculating.
It's not a theory, it's a guess. The cave man isn't working on a theory, he's not trying to prove himself wrong, he's just guessing, and without any work behind that, as you point out, he's speculating. There's literally no reason for anyone besides the cave man to think he's right, and his speculation has no impact on anyone else.
The reason it's special pleading is as follows. "All things abide by X, except this one thing." That in and of itself is NOT special pleading. The special pleading comes in when I ask for a demonstration. First, demonstrate all things abide by X. Great! Success. Now, demonstrate that this one thing is NOT in any way governed by X. Not say, DEMONSTRATE. Show. THe problem is there's nothing to show, because it 'exists outside of space and time', which even if it were coherent as a concept (as space and time are both required to meet the two basic conditions of existence), I must then ask "even if this one thing cannot be seen, can I at least see something else that exists outside of space and time, so that I can tell it's possible?" The answer is of course no, there's only one thing that exists outside of space and time. EVERYTHING else exists inside of it. The one thing is an undemonstrated cause, the only one of its kind, and cannot be demonstrated, it is exempt from conditions that literally every atom in the universe abides by...and is therefore 'special.' Using that as an argument without demonstrating ANY of it, basically to stop the chain of questions without earning that stop, is appealing to this unique specialness, or special pleading.