One other little nit-pick: if you ever end up doing this on a lot of files (e.g. as returned by File::Find or readdir), it will go noticeably quicker using the "_" (underscore) as a placeholder for "last file stat'ed" -- i.e.:

use strict;

my $file = shift;

if ( ! -e $file ) { die "no file" }

my $age = -A _;  # re-use the stat done by "-e" above

if ( -d _ )    { print "directory\n" }
elsif ( -T _ ) { print "probably a text file\n" }
else { print "probably a binary file\n" }

print "Before being read just now, $file was last read ",
    scalar localtime( $^T - $age*24*3600 );

# $age is in days, so multply to get seconds, subtract from
# script's start-time to get original file access time, use
# "scalar localtime" to print that in human-readable form
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Note that there may be limits to the reliability of the "-T" (and "-B") tests: they base their decision on reading just the first block or so of a file, but some files that seem to start with text data may contain "binary" (non-text) data later on... It can be a fuzzy distinction in any case.