Hi, Let me also extend a very warm welcome.:thumbup:
First lst me say congrats on a pair of fantastic watches.:001_tt1: The 116713 is a stunning reference with fantastic upgrades to an already storied model. Your 16610 is the classic Rolex dive watch made all the more special to many because of it's tritium dial. VERY well done!!:thumbup::thumbup:
As to the accuracy of your watch, a couple things if I may. Mechanical watches tend to preform differently for different people based on a number of factors. Our level of activity, how many hours a day the watch is worn, whether one wears the watch on the left or right wrist, etc.....
For me Rolex watches have a tendency to run a bit fast( the notable exception being my 116710). I've had several Rolex regulated and have found once properly regulated the watch can demonstrate superior accuracy. I think the key is to have the watch regulated for your wearing habits.
The reading one gets from a machine sometimes do not equate to how the watch will preform for you. My watchmaker that has serviced several vintage pieces( Rolex trained, parts account, etc.....) makes note of which wrist I wear my watch on (right) makes an adjustment and tells me to monitor the timing for a few days so adjustments can be made if necessary.
I have several vintage pieces (35 to 40 years old) that run within +1 to +2 seconds a day. My 16610 seems to run spot on, reguardless of position, after having been regulated in this manner.
Sometines we tend to confuse accuracy with consistency. A watch that is consistent is indeed a very accurate watch, if perhaps needing a bit of regulation for one's habits.
My experience, especially with the modern 3xxx fast beat movements, is that Rolex makes about the most consistent watch there is and can be regulated to amazing accuracy that unlike some will hold through very trying conditions.