This Part is controlled from an external keyboard set on MIDI Ch. 2.

Is keyboard control set to OFF for that part?

If I'm not mistaken when keyboard control is OFF for a part then, as you describe, the front panel controls will only operate if that part is actually selected.

One possibility is to duplicate that part 2 and have one of the dups use 3 elements and the other dup use the other 2 elements. Then have the external keyboard 'switch between the two different sounds'.

Another possibility is to:

1. select part 2 (where keyboard control is OFF)

2. press the assign switch to cause the element switch

3. press the 'home' icon to return to performance home and deselect all parts

Pressing the assign switch when the selected part has keyboard control set to OFF only affects that one part.

Another thing you can do is use ARPs to trigger turning on and off the ASSIGN switch.

1) Turn on ARP master and also ARP for Part 2

2) In individual ARPs for Part 2, change ARP 1 from Off to any of the "AF1" arps - it doesn't really matter which one (for ASSIGN 1) or AF2 (for ASSIGN 2).  There is an AF1 and AF2 arp - you probably don't need that, but if you do ... use it.

3) Under Common ARP settings, change ARP to "Hold" to ON.  "Loop" ON.  "Change Timing" to Real-Time (not measure).  Use Key Mode = Direct.  Change the note limit so that only the lowest key (or highest key) triggers the ARP.  This will replace the switch.  The highest or lowest key of your MIDI controller.

4) Under Advanced ARP settings, change "Toggle Mode" to "Toggle"

Now when you press the lowest key (or highest - wherever you limited the arpeggio note range) the assignable switch will toggle on and off. 

I haven't tested this yet (recently) with Keyboard Control=OFF Parts.  So I'm not sure if doing this will always toggle the "global" assignable switch or will stick to the individual Part's assignable switch.  I think it should toggle the individual Part when keyboard control is off.  And the external keyboard should toggle assuming you do not have this Part selected and Kbd Control = OFF.   That's my theory at least.  I'm sure someone will "test" and provide feedback.

I did test this out using the local keyboard.  I just didn't want to hook up an external MIDI controller (to test how it works externally) since my studio is ... not optimal at the moment.

Haven't been able to get that to work yet.

I haven't tested this yet (recently) with Keyboard Control=OFF Parts. 

I've tried several variations but so far I haven't been successful getting that arp 'trick' to work. 

There are some limitations with arps because how they "reroute" things and I haven't memorized all of those cases.   Lots of exceptions (in general).   I'll take a look and revise if necessary.

It works for Montage Classic.

https://soundmondo.yamahasynth.com/voices/122689

E0 as the trigger note is in Yamaha MIDI terms which is often a different octave than other manufacturers - so an external MIDI keyboard or software may call this a different E(num).

I used an iPad connected to the USB TO HOST port and used an on-screen keyboard set to the right octave to both trigger on/off the A.SW1 (only for Channel 2 - set your keyboard to MIDI channel 2).

Keyboard (MODX/Montage) must be in multi-channel MIDI mode.

Got it working using 'IA1_FolkRock AF1_N' arpeggio. It may have been an issue with the previous arps that I tried even though they had 'AF1' in their name.

Seems like a lot to go through to avoid 2 extra button pushes: 1) select part 2, 2) press AF1, 3) select Performance Home. I would have to really be out of alternatives to use an arp with a special setup just to do that. But, hey, whatever solves the problem.

There is no 'multi-channel' mode per se in the M models.

Keyboard (MODX/Montage) must be in multi-channel MIDI mode.

That mode went away. You basically deal with each part individually in how you want it to communicate with the outside world. 

In the M you designate a part as EITHER: 1) Internal or 2) External on the 'Edit Part n -> General / Pitch -> Zone Settings' screen (p.92 of the ops doc).

Check the Part Mode setting.
Select Internal to play the sound from the tone generator block, and External to play the
sound from the external sound module.
NOTE
You can also use a shortcut for changing the Part Mode setting. When [PART SELECT] is on, quickly
pressing the corresponding PART button twice (double-clicking) switches between Internal and
External settings.

Hasn't gotten me yet but I'm betting that an accidental 'double-clicking' is going to trip people up at some point when a part's sound disappears and you didn't think you did anything. Until I saw the above doc quote I doubt if it would occur to that I might have switched the part mode.

The change was needed but now it works differently than people are used to if they have a classic Montage or a Modx model.

OP has a MODX so my bias in instructions is towards that gear.  Lucky for me, I have a representative keyboard to provide help for those.   At any rate, good to have some additional notes on how to translate to M, if necessary.

In addition to my original suggestion - the soundmondo example uploaded also note limits Part 2's actual note range so that pressing the trigger key doesn't make a sound.  I wasn't originally concerned about this "artifact" but a well behaved actual use case would note limit the actual notes played so that pressing the trigger (note based arp toggle) doesn't make a sound.   

There's always a lot of ways to accomplish a goal - now the OP needs to sort out which one works best.

Didn't address the "extra button press" comment.  By default the Performance comes up without Part 2 selected.  So recalling this lets your external keyboard toggle [ASSIGN 1] (aka A.SW1 aka AF1) by a MIDI note.  There's no need to jump to any menus or select any part.  It just works.   The benefit is you don't have to map the external MIDI keyboard to send a CC message which is typically more difficult to setup and I suppose some external MIDI keyboards don't give you the facility.   Allows leaving Part 2 as Keyboard Control = OFF as we assume the OP has Part 2 already for external control of the internal tone generator.  

Personally I would probably leave Part 2's Keyboard Control ON, use the onboard switch, and octave shift the note range of Part 2 away from the keys (probably extreme upper range - beyond the notes of the MODX) and note shift Part 2 down (and/or element coarse) to get the notes back into range when addressed by "extreme high" notes from the external keyboard.   And be sure to note limit the Parts with local keyboard control so that these extreme high notes are not in the note range.