Resolution became possible by searching various parts of the system for instances of prng in a case-insensitive manner.
Preliminary investigation reveals that on similarly configured systems, but where one works, and the other does not, the configuration appears identical, but on the non-working system, a in.prngd service is not running.
# ps -ef | grep prng
root 350 1 0 Mar-23 ? 00:00:11 /etc/in.prngd /etc/egd-pool
Between both systems, configuration files, scripts, and binaries, in or under /etc seemingly related to prngd have identical sums, and a system software verify shows no automatically correctable anomalies.
Start scripts under /etc/rc?.d/ were identical, with prngd startup apparently handled by /etc/rc2.d/S85tcp. Examination of this file appears to indicate that the service is started by calling /etc/prngd, and /var/adm/rc.log seems to show the system attempted to start the service.
Starting TCP services: prngd inetd snmpd sshd ntpd
Attempting to manually use /etc/prngd to query or start the service fails with a similar error:
# /etc/prngd query
/etc/prngd: ^X: bad number
A copy was made of /etc/prngd, and set -x inserted:
+ [ -r /etc/prngd.lock ]
+ read line
+ set -- junk
/tmp/prngd: ^X: bad number
On the working system, /etc/prngd.lock is non-empty and contains the PID of the running in.prngd process. On the non-working system, the file is empty.
# rm -f /etc/prngd.lock