Dumb question about half damper sustain pedal


Hi I got a few dumb questions. The first one is, any midi keyboard supports half damper sustain pedals, right? It has nothing to do with the keyboard? The second one is, as far as I know, a half damper sustain pedal writes data like a fader or a mod wheel, its range from 0-127 and anywhere in between, instead of either 0 or 127, right?

So here is the thing, I just bought a Yamaha FC3A which I believe supports half pedaling, but it sounded like it didn't so I recorded a few bars with only using the sustain pedal, and all the values were 0 or 127, nothing in between. So I thought maybe my midi keyboard doesn't support it? or do I misunderstand how it works?