When Gnome shell extensions are disabled, Dropbox starts up properly, and shows the tray icon. But when I enable shell extensions that have an icon of their own in the system tray, then Dropbox either doesn't start at all, or starts without tray icon. Not clear. Apparently, it is fighting for a place in the system tray, but losing the fight.
Ubuntu 18.10 x64 with default Gnome desktop
Ubuntu software center reports that I have Nautilus Dropbox installed, version: 2015.10.28-1ubuntu2, source: ubuntu-cosmic-multiverse
I ran a few commands to get dropbox status etc. After running the last command, the tray icon still does not display.
Wanted to add this the issue is not just with Gnome extensions. I tried Mega sync, which has a tray icon, and I saw the same behavior. Mega icon displays, and Dropbox icon does not. Conclusion: Dropbox tray icon fails when other tray icons are present on Ubuntu.
Re: missing tray icon -- Ubuntu with Gnome shell extensions