It is all RNG, and if I read correctly somewhere, the items spawn when you land/disembark. If you grab them they disappear. If you leave them they get deleted on Thursdays.
It took me over 4 months but I have every G3+Optionals I will ever need plus some.
If this is the road you want to go down on, you will need lots of spare change in the bank. Most G3 items, with both optionals fitted, can cost over 12 million credits.
Use the Inara query below and just keep at it until you have what you want. Change "Near star system" to whatever you like. The less popular the better and sort the output by Updated descending. I chose only Outposts because the walking distance to the store is almost half that of Starports, and they seem to spawn better stuffs.
Hop in an Apex Shuttle, start at the top of the list and work your way down. Keep track of the visited systems in Notepad.
It's a great activity for relaxing after work. Grab some

, fire up YouTube for in-flight entertainment and enjoy the ride!
This method works regardless of server tick day because all systems listed "should" be unvisited. When you reach systems visited 21 days ago, change "Allegiance" to something else, hit search and repeat the process. It will give you a whole new list and should keep you busy for a week. If Apex complains about a distance just skip that one. Happy looting! o7
The companion site for Elite:Dangerous with the game database, market data, trade routes, outfitting, engineers, blueprints, crafting, Thargoid war, squadrons, logbooks, galleries, galaxy information and much more...
tinyurl.com
Edit to add:
If you want to be a helpful ol' chap, make sure to share any unwanted G3+ items you find in the
Pre-Upgraded Gear Sharing is Caring Thread.
(do this AFTER you left the system, so nobody beats you to any remaining goodies. You would be amazed at how fast some CMDRs can reach a shared location)