FWIW, the missing piece was this:

export PROMPT_COMMAND=jobs

which leads to the likes of this every time the bash prompt is displayed, e.g. after Ctrl-Z'ing a terminal app I've temporarily done with, but which I don't want to utterly exit:

[1]   Stopped                 digg
[2]-  Stopped                 mp  (wd: ~/bbs/final)
[3]   Stopped                 usenet  (wd: ~/News)
[4]   Stopped                 weblist
[5]+  Stopped                 vic z  (wd: ~/bbs/final)
xxxxxxx@xxxxxxx:~$