There is ambiguity in the term "to time a run". It can be running with your eyeballs on the watch all the time for pacing. Or pacing by feel without looking, but the time, distance, pace and everything else are recorded anyway and uploaded automatically when getting within the wifi/bluetooth range at home. It actually requires more effort not to do the latter if the watch you wear 24x7 already do this by default.
Being able to look at your pace and HR without emotional reaction or changing your pacing is something one can learn. The good HR (low = relaxed) and good pace (low = fast) numbers are always moving in opposite direction anyway, like a cost-benefit balance. Can't lower them both by concious effort in a single session (although both should improve over weeks with better fitness).