I got one of those swatters, too, with the same problems you describe. I de-batteried it and parked it in a closet. I figure if I ever again need a battery-powered source of highish voltage, that might suffice.
When I had horses I discovered a couple of things about flies. One was they would come in the garage sometime before dusk and park themseves, the most popular thing being vertically-hanging things, then in the morning I'd open the garage doors and most of them would fly out. I had my machine shop in 1/2 the garage.
That vertical preference thing fascinated me, so I rigged two stiff parallel wires close together, put like 400VDC on them and hung them up. Observation indicated they were possibly sensitive to the electric fields and would avoid landing on it. Disappointed, I was thinking of trying one of those pulsing electric fence chargers or rigging the HV source to a 555 timer to pulse every three or four seconds to give them a chance to land on their preferred vertical thing and get all comfy before a pulse. I never got around to it for some reason and just got along with fly paper hung around the garage.
In my apartment I noticed (when there were horses and they were a real problem) that for some reason they preferred a curved yellow part of the sink. Wasn't dirty or anything, there was just something about ir that was comfy for them.
I was surprised just the other day when I found one of those four in the OP resting on the same curved area of the sink. And this is at least 8-10 years after the fly plague due to the horses. So it looks like something in fly brains makes them like that part of the kitchen sink as well as vertical things and horse manure.
Go figure.
I think I'm rid of those four adventurers now, either by mechanical means or they expired. At least non of them have crossed in front of the laptop screen or the TV or past my ears.
(I found that when you use a fly swatter, it pays to not swing down on them to splat them, but just above where they're sitting and you can knock them down in midair, just as they're taking off in an escape attempt. Much more sanitary.)
Just off the wall during this four fly episode, I noticed there was something about the top of my laptop screen they liked, so I created a screen filled with yellow (like the sink) with a small image of a fly on it with MS Paint and left it on my computer while doing other thngs.
They didn't seem to pay any additional attention to my fly decoy.
No joy there.
