Hi @freetinker,
If you have run Dropbox application within the same desktop session there is no reason Dropbox tray icon to be missing. Otherwise, while Dropbox application runs on an other session (terminal or graphical) icon is not going to appear. The same is valid for all singletion applications.
To appears on current session you have to stop already running instance and start the application anew within the current session.
Hope this helps.