Thanks for the comments above. The key was to set the SSH_AUTH_SOCK variable at the head of the file. I have no use for the sexy perl code, though, since I will keep this constant. I can now run cron jobs authorized with SSHKeychain using the following crontab:

SSH_AUTH_SOCK=/tmp/501/SSHKeychain.socket
0 15 * * 1-5 /usr/bin/backup
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