Curious
The wiring diagrams in the Tiger Workshop Manual do not show the turn indicator switch as having the flasher function. They only show a "dipper switch". My Mk II has the floor-mounted dipper switch. If the turn signal switch has that capability, it was never wired up. I do recall years ago seeing folks sell the turn signal indicator switch with this function, as an upgrade. I do not have an Alpine workshop manual, so I do not know what the wiring diagram shows.
The Alpine parts manual does indicate that the turn signal switch was also a headlight flasher switch. See the attached snapshot of the Alpine Parts Manual.
The Tiger parts supplement does not list the turn signal switch, so one would expect that it is the same as the Alpine's. Yet, it does list two flasher switches (one for Mk I and one for Mk II). Again, see attached.