There are myriad tells on most 5 digit Rolex gold and two-tone Sub reps including shortcomings in the areas of dial font, text alignment, an oddly flat quality to the dial text on a reference where gens have a decidedly raised gilt effect (just like on the early gilt Subs from 20 odd years earlier) etc . A serious weak point with 4 digit and 5 digit Rolex reps has also always been the engravings between the lugs. Many reps have case engravings that appear laser etched rather than the panto engraved style seen on gen Rolex watches. And the detail on many older generation reps doesn't even extend to any effort at all between the lugs (i.e. blank or totally incorrect case reference numbers and serial numbers totally outside the range for any particular model). If what you have is a pre-2005 16613 (no ROLEX ROLEX ROLEX banner on the rehaut) you might expect the serial number to fall somewhere between the R598xxx from year 1988 and the D's from year 2005 ... and they don't follow on sequentially through those years but a quick Google would tell you if your serial number rings true for an early 16613.
Just going on the OP's low res. pics, the watch does look quite promising to me. Assuming that it is gen, be careful who you choose to clean up the case and bracelet too. Upon launch in 1988 the 16613 was one of the first new generation Rolex 'es with fatter lugs, quite a lot beefier than the 5513 / 1680 period. A competent Rolex experienced technician will work very gently with a case to greatly improve it .... a less experienced technician might just hit the polishing wheel with gay abandon , polish the shit out of those lugs and shave some serious value off the watch at the same time. The polished vs. unpolished thing is a huge consideration for fans of vintage and classic Rolex watches. I'm not saying send it to a Rolex Service Centre, I'm just saying check carefully that whoever you entrust your watch to knows what they are doing.