It always helps to give the year and model of your Alfa (I'm guessing that it's a spider).

If your's has headlights or taillights that share a housing with the turn signals (like the rear parking lights and turn signals in the same housing) then the issue is probably that the housing isn't well grounded. In that situation, the housing (which serves to ground both parking and TS bulbs) is at a few volts above 0V when the parking lights are on, so doesn't allow the TS circuit to pass enough current to trigger the flasher.

 

Sorry, '76 Spider 2000
You may have hit the nail on the head!
Prev owner did not ground either of the rear license plate lights. Will check this out first after I consult the wiring diagram to see what their relationship to the circuit is. A start anyways. Much thanks for this lead.

 

99.99% of the time the problem is insufficient ground. Try running a jumper wire with alligator clips from the battery neg to the housing ground lug.

 

Will be my first port of call - is easy enough to do. Thanks