Suppose you'd cut a fiberoptic cable with two razor sharp mirrors, reflecting the traffic out into your sniffing device and then back into the wire again. How fast would you need to get the traffic up and running again to not get detected? Also, I have no idea what tags to use. If someone would like to change them - please do so.
Depends on the protocol, but probably faster than you can blink your eyes. Especially in data transmission within a matter of milliseconds a different fiber will be selected.
Tapping fiber optic can be done by carefully bending the fiber just a bit sharper than it is supposed to, but won't work on monomode fibers which are commonly used over longer distances than a few 100 meters, because the loss of optic power. The real trick here is to dismantle the cladding without damaging the fiber.