A great time to use the false equivalence fallacy is when your rhetorical position is compromised and you haven't thought it through completely, or if you need to rally support from people whose views are only expressed through talking points or who can't come to a logical conclusion on their own.
One way you could employ the False Equivalence could be:
One guy tries to light his shoe on a plane and we all have to take our shoes off, but someone shoots thirty people and we do nothing to make it harder to buy guns?
See how easy? It feels righteous and seems to make a point, but is actually gibberish. First, removing and x-raying shoes is a perfectly harmless compromise, it doesn't prevent anyone from getting on a plane, it only marginally slows things down, and you don't even have to worry about massive doses of radiation with unknown effects. Second, it doesn't take into account how inconvenient it would be to have to take off your shoes to buy an assault rifle.
Another would be:
It should be as easy to get mental health treatment is it is to get a gun.
Again, pithy but nonsense. The Constitution says nothing about mental health, because the Founders knew that people who were mentally ill were chosen by God to be that way, and that it would be a waste of good leeches to suck the bad blood from them. If anything, it should be as hard as possible to get any health care, especially mental health treatment, because of the aforementioned choices of the Almighty.
Here's a Facebook favorite:
Drug control laws don't keep drugs off the streets, so gun rights laws won't keep guns off the streets.
Silly. Drug control laws are designed to maintain a large enough underclass to keep the wheels turning.
Every other civilized nation has some gun control laws, and the United States has twenty times more gun fatalities than all of them put together, therefore we should have some gun control laws.
Actually, this is a use of the "red herring" fallacy: the United States is not a civilized nation.