However, the (optional) accessory footswitch was very noisy, and frankly a distraction to me and my bandmates. Turns out, they decided to use latching switches, and that's were all the noise was coming from. Fortunately, the BeatBuddy works just fine with momentary contact switches, which are inherently much quieter. Like 20 times quieter, seriously.
Note: you'll need to set the footswitch option in the BeatBuddy:
1) Press down the Drum Set and Tempo knobs, to enter the Settings screen
2) Footswitch -> Configuration -> Type = Momentary
3) Footswitch -> Configuration -> Polarity = Default OFF
Check out these really nice, quiet, momentary contact switches, that I found on Parts Express:
Here are the original switches and wiring:
And here are the replacements: