A bit of background info here perhaps? Mostly anecdotal for entertainment, but quite relevant if you are trying to create a rivet texture as authentically as possible. As an aerospace engineer I learned my trade from the roots up. Rivetting is a basic skill that most aircraft mechanical people learn. So here are a few thoughts about real world rivetting:
On the outside of the aircraft you generally get to see solid rivets or break-head pop rivets (frowned upon, but useable in battle damage repair). a.k.a Tucker Pops. There are break stem and break neck varieties where the break neck leaves the hole in the pop rivet filled with the head piece of the rivet stem and the break neck where the stem pulls off further from the end of the stem and leaves a hole can seep into the fuselage behind the skin. The main reason an aircraft repair team or manufacturer never use the "Tucker Pop" variant is that break neck or stem - just think where the debris goes when the rivet is set. Even those break neck rivets can wear loose and allow the "plug" to end up as debris somewhere.
The main types are of course solid rivets and come in two basic forms - countersunk and domed head. The domed head types are used where thin panels are rivetted together, because a countersunk hole would not allow as much grip for the rivets. Where the rivetted panels are thick enough, the hole can be countersunk and the finished surface is then flush. Really good rivetters can set flush countersunk rivets so well, that when primed, filled and painted, you will hardly see any "outlines" on a new aircraft.
But whatever rivet type is used, the aircraft skin flexes and there will always be darker dirt circles as the aircraft gets older. This is because the rivets will stretch and lift allowing moisture and dirt to seep in between rivet and skin. Also a good touch for painters is to remember that the original rivets are often colour anodized to indicate what material they are made from and how they are heat treated before use. "naked" rivets come in grey, green, silver, purple etc. and these colour mean a lot. Therefore the more worn your aircraft gets, the more surface paint is worn away and you will notice - especially on the dome headed rivets - the various paint and rivet colours showing through. Base coat colour, acid etch primer, rivet colour. Admittedly this is less likely to be seen in private or club aircraft in the "civilized" world, but a really busy "Dirty Gertie" bush plane can get severely weathered and there'll be grunge either dripping vertically down under gravity if the aircraft is parked outside for longer times or slipstream grunge caused by the airflow.
I note that the bottom picture above has both "pop rivets" (probalbly actually avdel - see below) and "flush (countersunk) rivets" in use. The pops look freshly painted and the countersunk ones show white (a fresh repair perhaps? Not yet painted?) yet the aircraft texture is well worn and chipped. hmmm... I'd move the rivet layers dawn below the grunge and I would make the edges of the pop rivets a darker shade that reflect the apparent age/use of the aircraft. There's nothing really wrong with the white rivets; well, except for the fact there aren't white rivets. If this texture is showing a repair job, they'd most likely be purple (Aluminium alloy)
Oh, I could add that the "pop rivets" I just referred to are probably "avdel" rivets - these are greatly improved versions and do not loose the stem remnants when the rivet is set. Still, as a purist you'll find we don't like them much either.

Only a solid rivet is a good rivet.
...and more to the point this is praise for the decal system, because you don't have to paint/copy/paste thousands of rivets and then add the dripping grunge as many times.
...although I do often notice when a flightsim aircraft livery painter doesn't pay attention to other details like rivet pitch and land. (Hint at OP - said with a grin). Mind you, if you ever take a look at a wartime aircraft (WW2), the people who built the planes didn't have the time to set every rivet flush - ten seconds saved per rivet over a whole production line meant more spitfires in the air. As long as the rivet placing was more "ish" than "iffy", perfectly aligned rivets weren't always the norm.
Heavens! I have just remembered - it's been 50 years since I learned rivetting and I remember the heartbreak when the examiner came along with a hammer and punch, made a hole in my test piece and said "It's just been shot - repair it!"
Have fun and enjoy these reminiscences.