My recommended approach:

• find all log files you wish to search (e.g. messages, messages.1, messages.2, and so forth)
• order your list of log files from the most recent to the oldest, say in an array
• for each file in your list search for your string
• if you find your string, store it, but keep reading through the file in case you find a later occurrence
• return the last found string, but if you didn't find the string then continue on to the next newest log file

For ordering your files you could possibly do the following:

my @files = glob( "/var/log/messages*" );

# sort by mtime
my @sortedfiles = sort {
    ( stat($b) )[9] <=> ( stat($a) )[9]
} @files;
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You could, of course, attempt to start from the tail of the log file and work your way backwards, but that is very hard work and may be an unnecessary optimisation.