It seems one needs to be very gifted, which sadly I'm not.
Nope, you don't need to be gifted. Well, you do need the gift of motivation and perseverance, but that's about it.
Anyone who is able to ad-lib a nice fill in the appropriate circumstances has spent a lot of time doing the following beforehand in order for that to be possible:
- Listening to fills that other people do in similar circumstances.
- Experimenting with trying to replicate those fills and also creating fills of their own (even if they are just random notes at first!)
- Evaluating how well they did, remembering the things that worked, making adjustments to the things that didn't work, and then going back to listening and experimenting all over again.
So my first advice to you would be to simply
try playing something during those long, monotonous spots. Play anything at all. It doesn't have to be good. Just put your fingers on some notes and see if you like what happens. If not, try something else.
Keep at it long enough and you'll eventually get something that works. It might not be the best possible thing to play, but it won't be bad at least! More importantly, you'll have done some valuable practice and started to develop a new skill.
Again, everyone who is a good "filler" was, at one point, a lousy "filler" (no different from you) who did this sort work in order to become good.
There are a lot of tricks and rules-of-thumb that you will learn though. I'll give you one for free.

Notes from the major pentatonic scale often sound good over a major chord. So, over that first F major chord, you could try playing any of the following notes, in various combinations and octaves: F G A C D