So i just tried on mine, does behave very much as i would expect it to by just selecting the "Frame Sync Output" option on the BNC I/O Selection Menu.
Tested some Random FPS/ Shutter-Angle Settings, and connected it to my Trusty Hameg HM 412 Oscilloscope (easy enough with just an BNC Cable

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Shot some bit of Footage of that Test, and tried to include a Shot of the Camera I/O Settings, as well as the Recording Settings and Oscilloscope Settings for each test for a bit of reference to voltage and Timing.
Tested on 3fps, 60fps (Shorter and Longer Exposure), 10kfps.
all work fine for me.
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Only advise i could give right now would be to compare your settings to the one i used there and try again, those worked for me.
I also dont know what LED you are using, and what kind of output current this output is meant for, but if you use a too Powerfull LED, some Current Limiting circut could kick in, and output would always stay low (Overcurrent maybe looks like short circut for the Camera, so its always low). Oscilloscope obviously doesnt draw any substantial current, so voltage-wise the Signal is sure there on mine. If that turns out to be the Problem, maybe add some kind of Pre-Amp to it like some OP-Amp Circut, so the OP-Amp would provide the Current needed for whatever you want to drive with that signal, if you want to be sure.
Maybe a completely wrong guess from my side, but worth mentioning.
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Also in case you where not aware, shutter angle does affect the Output signal, so if your test is running at whatever FPS (lets assume 3), and your Shutter angle is set to 1° or 359°, your LED would then either be basically off or on the Whole time, and i dont know if the Hi/Lo indicator on the I/O-Settings-Page would even care to change for that short bit of time. Just FYI. if you didnt so far, try again with 180° Shutter.