The MASTER FX is global, all Parts of the Performance and the A/D Input that are set to “Output Select” = MainL&R will go through it. Only if you assign the Part to an Assignable Output can you not go through the Master FX.

When you want to assign control over when the Effect is in or out, you’d do best to assign it directly as one of the Part’s two Insertion Effect. You would then assign the “Wet/Dry” balance to activate and deactivate the Effect on that specific Part. Or you could set it as a System Effect (Variation) and then manage the Send amount as you desire. Here’s how:

Method 1:
When you set an Effect Type as an Insertion Effect, there is not going to be a Send amount. The Send/Return, found only on the System Effects, are exactly like the auxiliary Sends you find on a mixing console. Each channel on the mixer has a Send amount control.

Insertion effects work differently... example a Wah-Wah pedal is a classic ‘insertion’ effect. The guitar signal, and only the guitar signal, is inserted into the Wah pedal, the pedal’s output goes to the sound system... the pedal is literally inserted inline with the path to the sound system. No Send amount, necessary as all of the guitar signal goes through the device. You will find a “Wet/Dry” balance on those effect types where a subjective amount is allowed. On certain “utility” Types only 100% of signal is selectable (compressors, EQs, etc).

If you wish to use an Assign Switch to activate/deactivate the Effect, then setup as an Insert Effect and manipulate the “Wet/Dry” balance to do the job. Wet of course, is all effect... Dry is without effect. Some times, depending on the Effect Type in question you have a “Depth” parameter to control how much is applied.

Alternate Method.
Of course, you can use the Assign Switches to activate/deactivate send to the Phaser... as you know.

If you set the Phaser as a Variation Effect, then you will need to manipulate the Send Amounts of the Parts (to ensure only the Part that you want to use this communal effect, is actually using it). You can, on a per Scene basis, change the Send amount to the System Effects. You can pre-set the amount of Send from each Part, therefore you can manipulate when and how much of each effect is sent to the processor in question.

A Scene can store a “snapshot” of the Send amount going from each Part to either the Reverb or Variation Effect.
From the HOME screen
Tap “Scene” in the first colum
Here you can program the settings for the different MEMORY types.
By activating the MEMORY Switch over the MIXING category, you will be able to memorize the various mixing setting for each Part.
Under the “MIXING 1” option you can set the Reverb Send and Variation Send per each Part.

It can be different in each Scene 1-8.

Extra Credit:
Please this for mor details on the Scene “snapshots memory: Mastering MONTAGE/MODX: SCENEs

Hope that helps.

It helps. My biggest roadblock was VCM phaser doesn't have a Wet/Dry control.

Yet another option would be to use "duplicate" elements on AWM2 PARTs (assuming there's available ones) such that you have half of the original elements sounding with XA Control (A.SW1 ON, for example) and the other half - which are the copies/duplicates sounding also with XA control - but with say A.SW1 OFF.

Then you can keep VCM Phaser Stereo (or Mono) as an insertion effect and "bypass" it by selecting which set of elements are sounding.

In the effects routing page - say you have InsA as VCM Phaser Stereo and you have InsB as some Delay. And say Elements 1-4 make up the original sound (set with XA control sounding when A.SW1=ON) and elements 5-8 are the copies of elements 1-4 (set with XA control sounding when A.SW1=OFF). Still in the effects routing screen, you can direct elements 1-4 to target InsA (left hand side of routing diagram). InsA is the Phaser - so when A.SW1=ON, the VCM Phaser will be in the effects chain. You can direct elements 5-8 to target InsB. This will bypass the phaser so when you have A.SW1=OFF, then elements 5-8 will sound and the phaser will not be in the effects chain.

Some caveats:

1) Slightly more complex - more steps
2) You have to have the "room" in available free (unused) elements to make copies of the originals
3) If the copied elements are already using XA control to work - then this may not be compatible with the original programming which also depends on XA control. Best used on PARTs with no existing XA control assigned ("off" ).
4) If Performance uses both A.SW1 and A.SW2 already - for other purposes - either a different PART (XA control or just offset modulation = control assign) then this may not be compatible with the existing programming. Best if either A.SW1 or A.SW2 is already free. But that would be true of any use of the assignable switches - so presumably you already have this hurdle cleared.
5) This one is more subtle - unlike Wet/Dry - or a true bypass switch - using XA control is unlike either. When you switch - anything you are holding down from before the switch will continue to have the old phaser effect state applied. Say you had phaser OFF - held down a chord - then pressed the assignable switch to turn the phaser ON. The chord held would not change effects - it would continue to have the phaser=off. Only new notes struck after pressing the assignable switch will have the phaser=on.

... yet another alternative would "burn" even more resources - but is still a choice and solves caveat #5 above

Instead of making duplicates at the element level - you could make a duplicate at the PART level. If you have room to add another PART - you could copy the PART you want to turn phaser on/off. One copy would be "muted" when the assignable button is switched. Say you have any single-PART instrument in PART 1's slot and PART 2 is free. You can copy PART1 to PART2. Then set PART 2 so it has the VCM Phaser insertion effect and PART 1 does not. You can set the Volume of both PARTs to 0. Then in the control assign, you can assign an assignable switch - say A.SW1 - to offset the volume. PART 1 you can set to offset the PART 1 volume by +100 when the A.SW1 is OFF. And PART 2 you can offset the PART 2 volume by +100 when A.SW1 is ON. This way the phaser would "hard cut" between on and off. If you held a chord - the held notes would change having phaser or not having phaser applied. More like a true bypass switch.

Some caveats:

a) Slightly more complex (like the above caveat)
b) You have to have the "room" in available free (unused) PARTs to make copies of the originals
c) This method uses more polyphony since the PART which is at volume=0 ("muted" ) still consumes polyphony.

Note you could also do a variant on this second theme and instead of using the control assign destination offsets - you could use XA control but have PART 1 use XA Control of A.SW1=off and PART 2 as XA Control of A.SW=on. This would have the #5 caveat from the first additional alternate above - but you may want that. The benefit is that polyphony would be spared and would not consume more polyphony (no more caveat "c" ). You may want to do this if you didn't have room to make element copies but want to still spare polyphony.

Thank you both for the edit options.