I'm trying to understand the theory of relativity, but I keep getting stuck on the notion that objects/phenomenon farther away from the observer will seem to occur later than they really occur because the evidence of object (visible light, whatever) needs to travel a given (seemingly uncounted) distance.|||There is a fundamental misunderstanding in your question. You seem clear that there is a time when things 'really' occur. But in relativity, we find that there IS no agreement on when events occur, between observers in different reference frames. One will observe that "A" occurred first, another that "B" occurred first. And depending on the relative velocities of the observers, one will say that 4 seconds passed between events, one that 8 seconds passed.
However, it is not so much the raw distance that is the issue, but the relative distance, location and speed of the various observers.
It takes time to understand Special Relativity.|||That's all accounted for; don't worry about that. Assume that the people in the thought experiments with stopwatches etc. know perfectly well that light takes time to travel, and they account for it when they're looking at things happening.
Relativity is most definitely NOT about the time lag whereby, if you're looking at something one light-second away, you're seeing how it looked one second in the past. Those kinds of time lags are incidental distractions.
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