We are talking VII? no, just the ground for the flasher.
Some of the more modern Guzzis don't have a flasher at all instead they have 4 dedicated outputs from the dash.
I helped a guy with a Griso, his LEDs were still glowing even with the key out and he could measure 8 Volts across the lamp. I have a Griso so I checked into it, I don't have LED lamps but I stuck a couple in to try.
It turns out that the dash checks for a burnt out lamp, it tries to pull the output toward +12V to the tune of 40 microamps even when the ignition is off.
If the key is turned On and the output goes higher than 3.2 Volts which it will do if a lamp is burnt out the dash displays a picture of a lamp and the red triangle is illuminated. Some LEDs have a high forward bias that may cause the alarm, the Griso owner measured 8 Volts, this probably has several elements in series, The LEDs I have had 19 elements in parallel and the forward bias was only 1.97 Volts and operated without a problem.
Simply adding a 1K 1/4 Watt resistor across the lamp is enough to keep the Voltage down when not operating, the resistor should ideally be at the end of line across the lamp. Soldered across the lamp holder is probably the best you can do.
The V7 range have a different arrangement based on measuring the lamp current, i'm guessing you need a shunt resistor to run LEDs in this bike.