I won't be able to get out to my car until tomorrow evening, but I believe the flasher unit is behind the dash. It's parked for the winter in a position that makes it difficult for me to see under there, but I'll try and take a look. Failing that, I've got the manual out there with it, and maybe that will give a hint (unless someone else comes through with the location before then).
I believe I've read (probably on the board here somewhere) that a faulty emergency flasher switch will keep the directional signals from working as well. You might want to make sure the emergency flasher switch is actually hooked up.
I would also double-check to make sure power is reaching the flasher circuit before assuming the flasher itself is at fault.
Finally, since you're new here, you might not be aware that member Papajam has drawn up many Alfa wiring diagrams in glorious color, so much easier to use than the ones in the owner's manuals, and they're in the electrical forum. The one for the '71 Spider is here: http://www.alfabb.com/bb/forums/a/5405-10562-1750-spider-veloce-1971-electrical-diagram.html