Italian Mafioso
The Mafioso knows the Don and acts in the interests of the Italian team. They do not check for the Sheriff, but can win even after the Don dies.
The day position
Choose arguments that look independent and can be checked. Do not copy the Don's speeches automatically. It matters more to stay convincing over a long history of votes than to win a single argument.
Finding the Irish
Suspect those whose actions systematically help one gang and hinder another, but remember: similar behaviour can be explained by a civilian's mistake or by a false Sheriff's version.
The night choice
Weigh the consequences of removing a particular player for all three teams. Sometimes the most convincing civilian is a dangerous target, but sometimes keeping the city alive stops the Irish from getting a decisive numerical advantage.
Playing alone
After the Don dies, the right to shoot stays. Rebuild your priorities around survival, influence on the vote and control of the numbers; do not pretend that you have new checks.
Typical mistakes
Seeing yourself as secondary; saving the Don too obviously; taking an open accusation of the Italians as proof that the accuser is Irish.
In a pair
Do not turn into a public copy of the Don. Take part in the analysis, find the Irish and keep an independent cover story.
After the Don dies
Keep shooting at night without further Sheriff checks. Watch the numbers of the city and the Irish.
The endgame
Do not announce a win only because you are level with the city while the other gang is alive. Check the winning conditions for all three sides.