How to Parameterize Backup & Migrate to have both DBs saved?
There is a known issue (Too many connections in backup_migrate_source_db->_get_db_connection()) with recent versions of Backup and Migrate from 3.3 onwards which prevents CiviCRM from backing up as well is Drupal. If you use version 3.3 or later it is likely that you will not be able to backup the CiviCRM database as well as the Drupal database. However, you should still be able to backup the Drupal database.

I would suggest two possible workarounds:


Either uninstall Backup and Migrate and then reinstall an earlier version such as 3.2 or even 2.8.
Leave the latest version of Backup and Migrate in place and use it to backup the Drupal database only and set up a bash script that gets triggered by Cron to back up the CiviCRM database. This is what I am doing. The script I am using is:

#!/bin/bash

# Database credentials
user="username"
password="db_password"
host="localhost"
db_name="db_name"

# Other options
backup_path="/absolute_path_to_backup_folder"
date=$(date +"%d-%b-%Y-%H-%M-%S")

# Set default file permissions
umask 177

# Dump database into SQL file
mysqldump --user=$user --password=$password --host=$host $db_name > $backup_path/$db_name-$date.sql

#Compress the backup file
#7z a $backup_path/$db_name-$date.7z $backup_path/*.sql
gzip $backup_path/$db_name-$date.sql

#Remove the original sql file
#rm -I $backup_path/*.sql

# Delete files older than 30 days
#find $backup_path/* -mtime +30 -exec rm {} \;
find $backup_path/* -name *.sql.gz -mtime +30 -exec rm {} \;


for which I have set up a Cron job to execute every day.

Any debugging information you can provide for the issue will probably be welcome and help them in finding a fix.