Hmmm, I'd say not too fast action, even a medium action, Sorry Grouse
This is purely because a lot of pike flies are huge, waaay bigger than you'd use for Tarpon, and are often made from natural materials so they quite often weigh a ton. So, you need to cast with a slightly more open loop to give the lure time to turn around as trying to turn it with a sudden small loop makes the whole system really jerky and bouncy and hard to control. So as an example I tried casting pike fly on an Xi2, bloody nightmare, whereas an RPL was a much much nicer experience!
The 'Classic' pike rod much sought after these days is the Hardy Pike Rod by Ad Swier, and that would certainly be considered medium through action by todays standards.