Tooltip of current time

What I would like is as the user moves their cursor over the schedule either the left hand time highlights with the hovered time or a tooltip appears with the current time. Is that possible?

Could you please attach the screenshot how it should look like?
Do you know about the line marker for current time? Is this not that are you looking for?

The marker shows the current time of the day, but this would be similar but show the time for where the cursor is.

There is no inbuilt way to display such tooltip. You can implement it manually. To get the current cursor-pointed date please use getActionData method. Check there also ‘Tracking the cursor position’ sample.