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?