Your understanding of the half damper function is incomplete, yes the pedal is sending, but unless you have set the tone generator to respond you don't get any reaction. It's a two step function. The YAMAHA FC3 is the Yamaha pedal. (sorry, I don't know anything about Roland pedals).

You can learn about half damper function on page 111 of the Montage Reference Manual.

Or from this Motif XF article ...the Montage works the same way: Half Damper explained

"... you can make the "Half Damper Sustain Time" setting and level settings for the Amplitude EG, which determine how the volume of the sound changes over time. Also influencing this is the envelopes Release Time parameter. These can be used to control the change in volume from the moment a note is pressed on the keyboard to the moment the sound stops.

Unlike a conventional damper pedal control which simply turns sustain on and off, the Half Damper function lets you finely control the amount of sustain and natural decay-just as with a real acoustic piano-by using a continuous pedal controller. When the sustain pedal is released the decay time after the key is released is determined by the RELEASE TIME parameter. When the Release time is less than the Half Damper Time you create a very piano-like effect.

Just to clarify - the pedal doesn't send CC. The pedal changes resistance which the Montage/Motif, in turn, will respond according to the current settings (which may involve CC results).

When it comes to pedals (sustain, expression, etc) - the resistance (impedance) for any given action ("open", "closed", "full heel", "full toe", gradients of "half") need to match up what the keyboard expects. Often, between manufacturers, the expected impedance range is not the same. Also, there are other more subtle differences like the "curve" between "full heel" and "full toe" - like the expression pedal of Yamaha expecting a log scale while other manufacturers may expect linear (and thus release pedals with a linear response).

The properties of the pedals are often notated in the documentation. Note that the FC4 is not the continuous mode pedal. The FC3A is such a beast. Notice how the connector has 3 regions (TRS). ... I'm having difficulties finding the FC3A information, but from a user group (FC3 - which should be electrically the same):

Regarding the FC3: "The pedal outputs 10kOhms across the tip and center ring (open:~0.8, closed:~10.6)" note: 10.6 needs to be 10.6k. 0.8 I would assume is also in k which would be 800ohms - but possible this means 800mOhms - for now I'll just assume ideal values of "open" as approaching 0ohms and "closed" as approaching 10k.

I didn't find a great spec for the DP-10. Some claim tip and ring are reversed vs. what they expect - although I do not see a clear definition of reversed vs. what (FC3? some other pedal? certainly vs. the Nord's).

I did see a roland DP-8 documented (from a user) as:

"TIP-SLEEVE = 0ohm (open) to 10kohm (closed), RING-SLEEVE = 10kohm (open) to 0ohm (closed)" so it seems perhaps the POT resistance matches the FC3A for the DP-10 (assuming like the DP-8).

Further user discussion shows the Nord has "open" as infinite resistance and fully closed as 0.5k (on the Nord) - so perhaps the Roland also matches Yamaha in polarity.

I am only trying to see if the DP-10 is electrically compatible with the FC3A (which appears to be "OK" from what I can find thus far). Therefore, the keyboard settings (BM's advice) would be more applicable.