I was not a FAM (Federal Air Marshall) but, I was an Airport Police Officer, and did interact with FAMs on occasion. I honestly don't know what they do all the time, but did not want your question to go unanswered.
So, yes, without divulging trade secrets, you are correct. They have to target certain flights, because there are a lot more flights than there are FAMs. The reasons for targeting can vary. It can have to do with who is on the flight - people with connections to bad people, or, perhaps high profile figures - corporate executives, etc. Points of origin and destination also figure into it.
FAMs have to be polite, as they must coordinate with the flight crew to get the seats of their choice. I personally don't think flying around all day can be that easy. Remember, they have to stay awake and alert, without blowing their cover. Boredom is hard to fight! They also have to have a lot of self-restraint, in that they need to let the crew handle "disturbances" rather than jumping up right away to help out. The crew is trained to handle many things! And, they need to be a good shot.
I think it's a cool way to get to travel, so, if it interests you, I encourage you to look into it!