Well, you've got to be looking for something. The fact that the log message has multiple lines is immaterial. Given that the files are small enough to mail yourself, slurp the entire file and do a pattern match against the whole thing at once.

Relevant areas to look up: perlvar for $/, which, when undefined will cause the diamond operator to read an entire file into a scalar; and perlre for the /m and /s modifiers for matching newlines.