I have an old fence charger that does not pulsate and it will zap you even if you jump off the ground and grab it.
Can't figure that one out.
I hooked my Fluke 87 to it to test the voltage and smoke came out of the Fluke.
I had to peel many birds off of it.
They would land on it and ZAP they ended up hanging upside down.
So your problem got me thinking..can you hook some electricity to the feeder and flip a switch when the sparrows are on it and zap them all to their death.
Or maybe some remote fired something above the feeder that you can trigger while watching the birds.
Straight down shot into the ground.
I like your thinking!