Outside of explanations which state that multiple time dimensions exist it is difficult to show that a work of fiction has more than one. The key point that has to be established is that there is a kind of time that flows in a different direction than the past or the future or any of the spatial directions.
Things like timelines having time that passes at different rates would not qualify, as even the theory of general relativity already establishes that with just one regular time dimension time can flow at different rates in different places. Time flowing backwards in another universe would also not qualify it to have an additional time dimension, as it would still use the same directions of past and future as regular time, just with events playing out in reverse. For the same reasons, statements about independent time streams or of separate kinds of time, which could flow parallel to the original time, would not qualify.
Neither would dimensions that are timeless voids or are described as beyond spacetime in general qualify. Unless they contradict themselves, these realms should not have a time dimension at all, with change in them happening according to other principles. If they, on the other hand, do contradict themselves, the statement of them not having regular time would inherently not be reliable, making the idea equally unusable.
Of particular consideration are instances in which timelines as a whole are changed, such that there is a timeline (or multiple timelines) before they were changed and after they were changed or created / destroyed. As the timelines as a whole are changed, the before and after in this context can't be the past and future the timelines usually use, but should be a separate direction.
However, caution is necessary. As explained above, we require that the additional time dimension is "a line comprised of uncountably infinitely many points." If new versions of timelines are only created if they are changed, due to time travel for example, then the number of "snapshots" of the timeline would be far more limited. The amount of snapshots would be one more than the times the timeline was changed. So, for example, if the timeline is rewritten 2 times, there would be 3 snapshots of the timeline: the original, the timeline after the first rewrite and the timeline after the second rewrite. That are far less than the required uncountably infinitely many.
Aside from direct statements, the easiest way to confirm that the line is comprised of uncountably infinitely many points/"snapshots" is to show that the development of the timelines is time-like. I.e. typically one would want a statement indicating that the alteration of the timelines is subject to its own flow of time, or that special time travel can go to prior versions of the timelines instead of the past. The keyword in the latter case is time travel, as that specifies that the action happens through movement through something like time. Note that such statements can be considered contradicted if the fiction specifies that new versions of the timeline, i.e. additional snapshots, are only created when the timeline is altered or similar.
One other pitfall to consider is the case of branching timelines, where one can return to a past with fewer timelines by just going back to a point in the regular past that was before the split happened. In such cases one has to decide based on context if that is meant or if a prior version where the splits also didn't exist in the regular future is meant. The former case doesn't qualify for an additional time dimension, while the latter might if it meets the other outlined criteria.
