Use flock correctly. Use $0 not $BASH_SOURCE.

do-backup

@@ -1,5 +1,5 @@
 #!/bin/bash
-# Version: 0.1.0
+# Version: 0.1.1
 # Copyright (c) 2023:
 #   Darren 'Tadgy' Austin <darren (at) afterdark.org.uk>
 # Licensed under the terms of the GNU General Public License version 3.
@@ -10,11 +10,11 @@
 BACKUP_MOUNTPOINT="/localdata"
 RSYNC_OPTIONS=( '-a' '-H' '-A' '--timeout=300' '--partial' '--partial-dir=.rsync-tmp' '--delete-delay' '--delay-updates' )
 RSYNC_OPTIONS_VERBOSE=( '--verbose' '--stats' '--human-readable' )
-RSYNC_LOG="/tmp/${BASH_SOURCE[0]##*/}-$$.log"
+RSYNC_LOG="/tmp/${0##*/}-$$.log"
 
 # Sanity checks.
 (( $# != 1 )) || [[ -z "$1" ]] || [[ "$1" =~ ^(-h|-help|--help)$ ]] && {
-  printf "%s: %s <%s>\\n" "Usage" "${BASH_SOURCE[0]}" "backup definition" >&2
+  printf "%s: %s <%s>\\n" "Usage" "$0" "backup definition" >&2
   exit 1
 }
 
@@ -52,7 +52,7 @@ case "$1" in
     RSYNC_OPTIONS+=( '--contimeout=30' )
     ;;
   *)
-    printf "%s: %s: %s\\n" "${BASH_SOURCE[0]##*/}" "$1" "unknown backup definition" >&2
+    printf "%s: %s: %s\\n" "${0##*/}" "$1" "unknown backup definition" >&2
     exit 1
     ;;
 esac
@@ -60,15 +60,21 @@ esac
 # Only allow one copy of the script to run at any time.
 # shellcheck disable=SC2154
 if [[ "$FLOCK" != "$0" ]]; then
-  exec env FLOCK="$0" flock -e -n "$0" "$0" "$@" || {
-    printf "%s: %s\\n" "${BASH_SOURCE[0]##*/}" "flock execution error" >&2
+  # shellcheck disable=SC2093
+  exec env FLOCK="$0" flock -E 10 -e -n "$0" "$0" "$@"
+  ERR="$?"
+  if (( ERR == 10 )); then
+    # File is locked, exit now.
+    exit 0
+  elif (( ERR > 0 )); then
+    printf "%s: %s\\n" "${0##*/}" "flock execution error" >&2
     exit 1
-  }
+  fi
 fi
 
 # Source the mail configuration.
 source /etc/mail.conf "backups" 2>/dev/null || {
-  printf "%s: %s\\n" "${BASH_SOURCE[0]##*/}" "Failed to source /etc/mail.conf" >&2
+  printf "%s: %s\\n" "${0##*/}" "Failed to source /etc/mail.conf" >&2
   exit 1
 }