Si,
If you provide the method by which when a tiddler is opened in the story river you could include an action that sets the clock by setting a date/time field to now.
By default there are multiple ways to open something in the story view, via contents, the result of a search, following an "in tiddler link", from the sidebar or a button using "to=".
This could provide a method to add an action to all the navigation methods.
In the mean time, I recently discovered I could identify the last opened tiddler, in the story, what I call the "focused tiddler". Macro and sidebar attached.
The thing I like about this little macro is if you have a lot of tiddlers open, it is easy to return to the one with focus. I intend to add a button that focuses the current tiddler with a click if not.
I did see somewhere the ability to invoke an action when a tiddler changed. Perhaps you could find that and use this focus tiddlername.field to trigger what you want on the focus tiddler? I would however consider not allowing this for shadow/system tiddler or saving the time stamp for last read independently of the tiddler so it could operate on shadow tiddlers without editing them.
Regards
Tony