I have a (somewhat) clearer picture in my mind about this SystemTray issue.
It appears that Gnome has decided that the world does not need anything like the SystemTray, suggestions to the contary invoke a "that conflicts with the plan" - which in gnome speak is a very serious offence.
https://bugzilla.gnome.org/show_bug.cgi?id=652122Ubuntu, while playing with Unity, decided the SystemTray was getting messy and needed reinventing, they came up with the App Indicator App -
https://wiki.ubuntu.com/DesktopExperienceTeam/ApplicationIndicatorsWhich seems to be about providing a way to allow several processes to communicate via one icon on the panel.
Ubuntu seem to have carried that model forward to Ubuntu Gnome 3 based 18.04
There was an apparently unsuccessful push to get the App Indicator model into Gnome itself, it too was resisted. The Plan has Spoken ...
As there is a class of applications that need this sort of functionality, there are several Gnome Extensions that restore normal behaviour. But some are on the verge of being abandonware.
So, in summary, the Lazarus SystemTray Icon uses the original System Tray model, nobody except the users and their programers like that one. We could update it to App Indicator and it might work then with (eg) newer Ubuntu but Gnome will still disapprove.
Or we could tell our end users to use Ubuntu Mate
This is a challange for a development env that claims to support Windows, Mac AND Linux.
More research is indicated .....
Davo