If you are just burning fuel you follow a smooth track, if you are actively tracking signals, looking between buildings etc the flight pattern will be spastic as all hell to optimize your ability to see/track/listen..
You can shove all kinds of things into a plane not typically used for signals and intelligence, with the added bonus of it not looking like an AWACS or E3...
https://globe.adsbexchange.com/?icao=ae27fd
Like this pattern?
Don't know about that one, could be checking on a bouy or running surface(as in rescue)searches for a boat at the center of that.
These are 2 good examples.
San Antonio
https://globe.adsbexchange.com/?icao=ae056f
Oklahoma City
https://globe.adsbexchange.com/?icao=ae11ea
that C5 one fascinates me. That's an awful big bird to be flying like that. (not a veteran, just grew up near Fort Knox and hubs was 6 yrs US Navy) Thought they were primarily troop/cargo transport?
just write in the type in bing or something, will usually get you the wiki for it(not that wiki is the paramount of truth or anything.... but generally accurate about stuff like this)