Você pode usar o comando stat:
$stat -c --%x file or symlink
Ele não muda, apenas informa o último horário de acesso
man stat
NAME
stat - display file or file system status
SYNOPSIS
stat [OPTION]... FILE...
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%w time of file birth, human-readable; - if unknown
%W time of file birth, seconds since Epoch; 0 if unknown
%x time of last access, human-readable
%X time of last access, seconds since Epoch
%y time of last modification, human-readable
%Y time of last modification, seconds since Epoch
%z time of last change, human-readable
%Z time of last change, seconds since Epoch
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