I believe I found a solution, so I'll post it here in case someone else has a similar problem.
After install, I saw a warning message that I must have missed before:
WARN: Public service at http://alpha/searx is not available!
WARN: Check if public name is correct and routed or use the public IP from above.
Solution after install:
(1) Edit /etc/searx/settings.yml
sudo nano /etc/searx/settings.yml
(2) Change bind_address to the local IP of your host.
server:
port : 8888
#bind_address : "127.0.0.1" # address to listen on
bind_address : "192.168.0.73" # address to listen on
(3) Edit /etc/uwsgi/apps-available/searx.ini
sudo nano /etc/uwsgi/apps-available/searx.ini
(4) Set "http" to the local IP of your host.
#http = 127.0.0.1:8888
http = 192.168.0.73:8888
(5) Restart uwsgi.service.
sudo systemctl restart uwsgi.service
This allows access to the searx instance on my local network.
N.B.
During install, the script was unable to create the necessary directories for uwsgi configuration files. Here are the messages:
INFO: BUILD template /opt/searx/cache/etc/uwsgi/apps-available/searx.ini
mkdir: cannot create directory ‘/opt/searx/cache/etc’: Permission denied
./utils/lib.sh: line 436: /opt/searx/cache/etc/uwsgi/apps-available/searx.ini: No such file or directory
chown: cannot access '/opt/searx/cache/etc/uwsgi/apps-available/searx.ini': No such file or directory
INFO: install: /opt/searx/cache/etc/uwsgi/apps-available/searx.ini
install: cannot stat '/opt/searx/cache/etc/uwsgi/apps-available/searx.ini': No such file or directory
I created the directories manually and ran the install script again.