As usual RC is correct. the spot he pointed out is the most effective POA for gators. I have been involved with alligator harvest since 1973 when the first seasons were opened in LA. I worked on national wildlife refuges that allowed gator hunting for 31 years until I retired in 2014.
Regarding caliber a 22LR HP is most effective on gators 7ft and smaller. all though larger gators can be killed with a 22LR it is advisable to use larger calibers like 22mag, 30calM1, 30-30, .357 and the like. if you were restricted to one gun a 22mag with CCI maxi mag HP or the like would be a very good choice.
Large gators have a very thick bony skull , it is common for a 22 bullet to ricochet off a gator. it is also not uncommon for gator hunters or helpers to be hit by bullet fragments and bone . the angle of the shot needs to be as perpendicular to the skull as possible to prevent ricochet.
It is accepted practice and prudent to sever the spinal cord right behind the head of gators with a knife to prevent thrashing and nerve activity after putting them in the boat.
RC is correct again body shots to a gator will do nothing except piss him off and he will get away.
Contrary to what is seen on Swamp People there is usually not a lot of thrashing and drama associated with dispatching a gator. the gator is on a strong line with a big hook in his mouth. the gator is gently pulled to the surface and shot in the spot behind the eyes in the top rear of his skull-- normally No dramatic hollywood music and thrashing. the last thing a gator hunter wants is thrashing because the line can break, the hook could come out and the gator will escape!! please don't believe all the hyped hollywood drama you see on swamp people!!
American alligators are not crocodiles they do not normally prey on humans. However occasionally they will attack swimmers and children playing along a shoreline. If I were in a self defense situation with a gator, a 12ga shotgun with buckshot would be my weapon of choice. I would aim for the top of his head. Gator hunters don't use shotguns because that would tend to damage the hide which is valuable.
Bull