I was in that game you just mentioned. I was doctor and died healing you on n1So over the year's I've been the facilitator of many different styles of gambits. Long story short, most of the gambits I've tried have worked out for me, and my reads. However the way other players seem to interpret the gambits, make them kind of pointless. A lot of times even with good explanations as to who, what, where, when, and why players don't want to see where you're coming from they see "gambit" and associate it with deception, and most players associate deception with scum. Also as Oberon did mention, I'd say roughly 85% of players I've played with don't want to be persuaded by anyone else and if it doesn't align with what they themselves are thinking than the argument will be regarded as moot.
Now if done right and a good explanation is given as to why you performed the gambit and what you got out of it is key if you are going to do it. I would say involving other players like hard claiming fake claiming a red check on someone, or hard claiming a role you are not as town seldom work, and are selfish plays, that should be avoided imho. Now softing a check or something similar like that if done correctly can be pretty good to test reactions and such, but it should be brought to light later on that day with explanations.
So there was once a game where I pulled a sort of gambit where I acted like I had some more information then some other players. The setup was hidden, so I had a little wiggle room here. I basically gauged everyone's reactions to what I was saying and how everyone interacted with me. I was able to find the general town reactions and tones along with the shady scummier reactions and tones. Then you compare and contrast peoples metas and boom! I then came clean with what I did and why I did it, and my conclusions from doing it. I had a POE of all the town members and the 4 Scum in the Lynch POE. This was Day 1. Long story short nobody really agreed with my reads, ended up lynching elsewhere after I perished, left mechanically confirmed Mafia alive, and ended up losing the game.
All in all pulling gambits from my experience in the trenches end's up with town losing more often than winning.