Need Help with GMT II - Question

[turbineboy]

My first post here.
I am not sure if this post belongs here, but here goes.

I currently own a GMT Master II I purchased from a dealer/store in 2002 and my grandfather’s Rolex from 1939 which was passed down to me. I am looking to add to this and was presented with an opportunity to purchase a Rolex GMT Master 2 – in Two tone by a local seller / private owner.
As I have not purchased a preowned watch like this before, I am asking for some guidance/advice/help.

The private seller has a box, but no papers. He has offered the serial number/Model# (16713) and is offering the watch for a reasonable price.
The watch itself seems to be in good condition and he came with me to the local Tourneau store where they checked it for water seals and said it was running good and held to within 1 second timing. I am not sure what the “held to within 1 second” meant, but presume it can’t be all that bad.
The bracelet appears to be in good condition and comes with the two extra links the owner had to remove to fit his wrist. The bezel black inlay has some very minor scratches noticeable upon close examination.
I can upload pictures of the watch if that would help.

My question is regarding the serial number. I looked up several web pages that told me this watch is a 2004 production year.
How does one use the actual serial number and find the history of the watch – as in is it legally sold, how many times has it been in for service, has any factory service been done on this timepiece, is it actually registered with Rolex to authenticate it is not a fake, etc. etc. Does anyone keep track of this ?

Any help appreciated.

TY