Too bad we don't know the "cooling period" (if there is one) after new HGEs appear in a system. When I do my Imperial systems "pilgrimage", I simply select the ones with population around the upper scale (yes, I know some people say that it does not matter) and simply go random starting on Achenar. Most of the time, yesterday systems that were full of HGEs, don't have anything today, but there are others that now have spawns. Do not expect today to find HGEs in the same system that you found yesterday.
The only rule I found is that the distance from the star of the HGEs in a certain system seems constant: there are systems that spawns HGEs at ~2000ls and there are systems that spawns them around 50,000 ls (this is just an example). Also there are 2 timers: 20 minutes and 40 minutes, most being 40 (so if 20 may be the product of a 40 timer that decreased and randomness instead of a true timer, the max timer of 40 is 100% sure).
I don't think that the spawning (not talking here about the content) is pure random, there are some basic rules. Also, if you are in a system with 2-3 HGEs, try to plan the order of collecting them according to distance and timers and don't forget to either go back to the Nav Beacon and scan again after you clean the previous ones (or use FSS if the system is spawning them far away from the star). Many times I found more HGEs in the same system. Of course, while still possible, I use the "exit to desktop" method on HGEs with enough timer.
What I also found is that the content on a certain HGE spawning is fixed. There is no random content: if another HGE appears in the same system/faction while I'm still there or if I go to a material trader and return after a short time, the content is exactly the same.
I wonder if Frontier will ever rework the mechanic and allow us to be able to select the desired state on the Galaxy map and check the systems... Since in theory an HGE depends on a faction that may be in a different state that of the controlling faction, I wonder whether we may have in the future the possibility to use a filter that searches for factions in a desired state on the map. Of course, even this mechanic is currently broken, but I cannot complain too hard, since I have never had such an abundance of materials. And my play time is very limited.