I've been using and teaching EFT successfully for over 8 years. It works about 95% of the time for me and the other folks I've worked with. Even the sceptical ones. I had anxiety/panic attacks that were so bad I would crawl up in a ball, cold sweats, couldn't breathe, chest pain, and would pray for God to take me home. Got checked out at the ER, no heart problems, but the anxiety persisted for months. Finally tried EFT for about 10min after reading the manual. 80% of my symptoms vanished in 10min. The rest dissipated over the next few days as I worked on whatever emotions/physical issues came up. Got advanced EFT certification over the next year and began training others. I'm still amazed how well EFT works everytime I use it.
BTW you can use general tapping without focusing on anything specific but it may take you a little longer to get rid of the phobia. Try it both ways and see if there is a difference for you.