I have no idea about adding a beeper to the signal circuit. (I would not like that noise)
I too (and for a long time) have a problem forgetting my signal is on. Which pisses me off. I've had self cancelling signal bikes, but no more. The signal light is dim on standard or interstate, and I'm watching the road anyway. The only time you can't miss the signal light is at night, and I almost never do that anymore (old bifocal eyes, hate headlights, and drunks).
So, for a long time, I mostly don't use my signals, I use my old-school arm (which stops signalling right away. LOL) And when I have to really get on the brakes, my left arm goes straight up with clenched fist (even though I have extra brake lights on both interstates).
However, on left turns across traffic where I'm worried about busy oncoming traffic, I do use the signal for safety and better visibility. And left it on yesterday for 5 minutes or so.

Another trick I use, is to pop the signal on, cover the button with my thumb, and only let it blip 2-3 times (usually for just one car).
The cell phone driving, texting, GPSing, talking era is now well entrenched (despite the illegality). You can no longer assume anyone is actually watching for signals of any kind.
My best trick for this perpetual riding hazard is to ride for space. I go slow or fast to achieve my own space in traffic, and then work to keep that space, if I can. I'll use the monster torque and go 20 over for 5 seconds, then ease off and ride alone, for awhile. Then you get the guy in the 911 Porsche who thinks you want to race.