Here's the answer from level 2 Tivoli support:

Over 1 minute of the mount time is used to query the drives via ACSLS. All
the drives are queried twice - once to see if there is an available mount
point, and again to verify that the mount point is still available. Since
ADSM is multi-threaded, another mount could have taken place in the mean
time - or another system may have requested a mount from the same library. I
assumed, but didn't verify, that the more drives you have, the longer it
takes.

Part of the reason that this querying process takes so long is because the
ACSLS API is not multi-threaded. The Tivoli support person said that it is
rumored that STK is working on a multi-threaded API. When/if this is
available, the *SM developers will look at improving the performance. In
other words, it will be quite a while before this is fixed.

Thanks to all who replied to my original message. I hope this helps some
other folks out there.

Patrick Varney
Network Specialist
Pacific Gas and Electric Company
Internal 227-2823 / External 707-436-2823