It seems as using data frame times is possible when you have some time-enabled layers added to a map. Is it the case?
There is a time dynamic text tag. Thought what would happen if you'd combined the format parameter of the time tag with the dyn type "data frame"?
"Time: <dyn type="dataFrame" name="Layers" property="time" format="hh:mm tt" emptyStr="[off]"/>"