Use the disk archiver (DAR) to perform a full backup every other month, otherwise create an incremental backup.

etc_cron.daily_backup

#!/bin/bash

source /etc/default/backup

MONTH_TWO=$(date -d "- 2 month" '+%Y-%m')
MONTH_PREV=$(date -d "- 1 month" '+%Y-%m')
MONTH_NOW=$(date '+%Y-%m')
DATE=`date +%Y-%m-%d`
HOST=`hostname`

backup () {
  if [[ -z $MOUNT ]]; then
    echo "Usage: $0 DEVICE MOUNTPOINT"
    exit -1
  fi

  mount "$DEVICE" "$MOUNT"
  if [[ $? != 0 ]]; then
    echo "Cannot mount $DEVICE to $MOUNT"
    exit -4
  fi

  if [[ -d "$MOUNT/$HOST.$MONTH_NOW" ]]; then
    ROOT_DIR="$MOUNT/$HOST.$MONTH_NOW"
    echo "$ROOT_DIR exists, performing incremental backup"
  elif [[ -d "$MOUNT/$HOST.$MONTH_PREV" ]]; then
    ROOT_DIR="$MOUNT/$HOST.$MONTH_PREV"
    echo "$ROOT_DIR exists, performing incremental backup"
  else
    echo "Deleting expired archive at $MOUNT/$HOST.$MONTH_TWO"
    rm -r -f "$MOUNT/$HOST.$MONTH_TWO"

    ROOT_DIR="$MOUNT/$HOST.$MONTH_NOW"
    echo "$ROOT_DIR does not exist, performing full backup"
    mkdir -p "$ROOT_DIR"
  fi

  BACKUP_DIR="$ROOT_DIR/$DATE"
  INDEX_DIR="$ROOT_DIR/index"
  LOCK_FILE="$ROOT_DIR/backup.lock"

  if [[ -e "$LOCK_FILE" ]]; then
    echo "Another backup is currently running - lockfile exists!"
    exit -3
  fi
  touch "$LOCK_FILE"

  if [[ -z "$PASSWORD" ]]; then
    read -s -p "Archive Password: " PASSWORD; echo
    read -s -p "Confirm Password: " PASSCONFIRM; echo

    if [[ "$PASSWORD" != "$PASSCONFIRM" ]]; then
      echo "Passwords do not match, exiting"
      exit -2
    fi
  fi

  # Backup the home directory in chunks that most mount points can handle
  echo "Creating backup directory $BACKUP_DIR"
  mkdir -p "$BACKUP_DIR"
  mkdir -p "$INDEX_DIR"

  for HOME_PATH in /home/*/
  do
    INDEX_NAME=`basename $HOME_PATH`
    INDEX_PATH="$INDEX_DIR/$INDEX_NAME.index"
    BACKUP_PATH="$BACKUP_DIR/$INDEX_NAME.$DATE"

    if [[ "$SKIP_INDEX" == *"$INDEX_NAME"* ]];
    then
      echo "Skipping $SKIP_INDEX"
      continue
    fi

    echo "Backing up $HOME_PATH"
    if [[ -w "$INDEX_PATH.1.dar" ]];
    then
      echo "Existing index file found, creating incremental backup $INDEX_NAME"
      dar --alter=zeroing-negative-dates -w -v -D -K "twofish:$PASSWORD" -s 2000M -A "$INDEX_PATH" -R "$HOME_PATH" -c "$BACKUP_PATH"
    else
      echo "No existing index file found, creating full backup $INDEX_NAME"
      dar --alter=zeroing-negative-dates -w -v -D -K "twofish:$PASSWORD" -s 2000M -R "$HOME_PATH" -c "$BACKUP_PATH"
    fi

    dar -w -J "twofish:$PASSWORD" -A "$BACKUP_PATH" -C "$INDEX_PATH"
  done

  df -h
  rm -f "$LOCK_FILE"
  umount $MOUNT
} >> "$LOGFILE"

backup

etc_default_backup

PASSWORD='supersecrettimes'
DEVICE='/dev/disk/by-path/pci-0000:00:00.0-usb-0:0:0.0-scsi-0:0:0:0-part1'
MOUNT='/mnt'
LOGFILE='/var/log/backup.log'
SKIP_INDEX='folder_to_skip'

etc_logrotate.d_backup

/var/log/backup.log {
  rotate 10
  size 10M
  compress
  missingok
  notifempty
}