OK, Since posting I have been seeing a mix of appearing and not appearing, but I have had to use the software on the only machine on which we have 10.1 installed, so there has not been a lot of time for experiments.
1. It seems the first time I run the ArcMap and run a tool, the Marquee does not appear - nothing shows.
2. When I turned off background processing, closed ArcMap, opened ArcMap, turned on background processing - the Marquee showed.
I can experiment later - my gut tells me it has something to do with the first time the BG processing is running in a given ArcMap session - unless you mess with the option checkbox?
No percentage complete - I guess that is by design now?