Several have responded with ....

 The first thing to use is DBUTIL using the SHOW  basename USERS.
You must be logged on as the creator, or have a database maintenance word
assigned and use that.

 But in this case we are working across multiple accounts with a single
program listening for requests from our web site.  The web site is pushing
us towards 24 x 7 access, but we still have nightly batch processes that
must take place each business day.  Since these batch programs used to have
exclusive access to a production database in their account, and the roots of
most reach back 20 + years, the DB opens are not consistent.  Assuming the
DB is already open we'd like the listening program to find with which mode
the DB was opened and then use the compatible open mode, 5 or 6.