What I did (on my EC2 instance):
a) Followed Amazon’s instructions here to install their special PHP Memcached Extension for ElastiCache.
b) Confirmed it was installed and restarted apache
$ php -i | grep memcached
/etc/php5/cli/conf.d/memcached.ini,
memcached
memcached support => enabled
libmemcached version => 1.0.4
memcached.compression_factor => 1.3 => 1.3
memcached.compression_threshold => 2000 => 2000
memcached.compression_type => fastlz => fastlz
memcached.serializer => php => php
memcached.sess_binary => 0 => 0
memcached.sess_consistent_hash => 0 => 0
memcached.sess_lock_wait => 150000 => 150000
memcached.sess_locking => 1 => 1
memcached.sess_number_of_replicas => 0 => 0
memcached.sess_prefix => memc.sess.key. => memc.sess.key.
memcached.sess_randomize_replica_read => 0 => 0
Registered save handlers => files user memcached
c) Confirmed I could send and retrieve objects using the script here (I could).
d) Updated wp-content/w3tc-config/master.php with the full address and port of my ElastiCache instance wherever it was pointing to 127.0.0.1:11211.
e) Tried and failed to figure out why I still can’t select Memcached from the w3tc dropdown.