Is there a symbol which is generally recognized as a connotation for time?
For example...
Dollar Amount = $
Count = #
Time = ???
In this context, I am simply adding up the duration of a number of events. The events are measured in seconds...but the units used on the sum total of the events will vary depending on the level at which the user is reviewing the data (could be seconds, minutes, hours, days, etc). So here I am not really trying to express the units per say, rather the larger category of time.
What about Eta (η)? In cosmology, η represents conformal time...but this feels like a stretch.
As has been said in comments: $t$, $T$, and occasionally $\tau$ are common. Maybe with subscripts e.g. $t_0$ or other modifiers.
However, mathematicians are more relaxed about consistency of notation than physicists. You could use pretty much anything you like as long as you say so. Even if you use $t$, don't assume that your reader will know that it means time. Maybe in physics, you could write $V = I R$ in an electronics context with no explanation but in mathematics that is less advisable. Probably the most consistent notation in mathematics is $\pi$ for the circle constant $3.14159...$; I have not seen anything else used in any vaguely recent book or paper. However, even $\pi$ is occasionally used for other purposes.