At some point in time the BeatBuddy footswitch had once been of a latching type and later was changed to momentary. Is there a highly unlikely remote chance you might have an older one that is latching? Did the ‘whole new setup’ that Singular sent include the footswitch or just the BeatBuddy?
You mentioned the Yamaha sustain pedal that works. If you have a sustain pedal input on your keyboard, try the Yamaha pedal and see if that sustains correctly and then try the BB footswitch and see if it also sustains when depressed and releases when the switch is let go (only one switch on the footswitch will do this). The TRS cable should work OK to do this (i think), but a TS cable could be tried as well.