is there a setting available (Utility?) to only Run & Send the Clock upon pressing the Arp On/Off switch?

No.

The MOXF Arpeggiators follow the Clock of the MOXF. If the MOXF is a slave to external clock all MOXF tempo driven functions will follow that external tempo.

MOXF Clock Out
If “Clock Out” = On this means the MOXF will always be sending clock messages Out via MIDI. Any external receiving device can ‘see’ this clock. External devices ‘see’ the Clock messages (F8) streaming from the MOXF... but they do not do anything, necessarily. In order for the receiving device to Start, for example, you must press the Transport’s Play button which sends a command (FA). A receiving device will respond by running whatever it has that responds to clock. For example, the FA command would tell an external sequencer to run. (Just the existence of Clock does not *start* anything).

If the external sequencer is additionally set to MIDI SYNC = MIDI, then it will run at the Tempo as set in the internal MOXF.
If however, MIDI SYNC of that external sequencer is not set to MIDI SYNC = MIDI, the external device will run at the tempo of its own.

FA, FB and FC are the universal MIDI commands for Start, Continue and Stop, respectively.

These commands do NOT affect the Arpeggio, at all.
Arpeggios can follow the tempo of the MOXF Clock, and if the MOXF is set to MIDI SYNC = External or MIDI, the MOXF will look to the external Master Clock for tempo. You may also see a setting for “Auto” for MIDI SYNC — this allows you to use the MOXF Arp without having to run the external clock (like when trying out what you want to play).

If the MOXF is slaved, all MOXF clocked features will follow the MOXF Clock as they always do. These include the Arpeggiators, the Tempo driven Effects, and Tempo driven LFOs.

So no matter what, the MOXF Arpeggio follow the Clock of the MOXF... whether it is master or slave, the Arps always follow the MOXF.

But the Arpeggios do NOT START (FA), nor do they CONTINUE (FB), nor do they STOP (FC) in response to these standard MIDI commands. Arpeggios require an additional “musical input” to be used.

By “musical input” we mean NoteOn events — that NoteOn event tells the Arpeggio when to start and gives it instructions as to what to play.

Just because you press a START button do not expect the Arpeggiators to do anything. You must additionally use a musical command.

Starting a Sequencer requires no particular skill — Starting an Arpeggio require musical skills
Anyone, including your pet cat, can jump up and press the Sequencer PLAY button to start a sequencer playing back.
But some musical expertise is required to start an arpeggiator. The NoteOn must be musically correct so the Arp Phrase selects and plays the right musical phrase, and exactly when the NoteOn occurs is significant.

If you press a triggering chord, G7, to start a guitar strumming Arp phrase, if you hit it on the downbeat, the Arp phrase will start right there, but if you hit that triggering chord an eighth note after the downbeat, the entire Arp phrase will be time shifted late by precisely an eighth note. It will be in Sync but offset by the eighth note. (This allows Arp phrases to be turned ‘inside out’... )

This is a feature of Arpeggios, they can be offset by precise amounts depending on when exactly you press the triggering chord.
So your cat will need to know what notes to hit to get a G7 to sound and it will need to be able to trigger that voicing at the appropriate moment in the musical count.
Skill is involved... because Arps are musical... no skill required to send a Start command, musical skills required to operate an Arpeggio.

Remember, the Clock is always running... like the clock in your Smart phone... it is always running. You may have an App that is a Timer, it will reference the phone’s main clock, (for minutes and seconds) but the Timer App has a separate command which is needed to have it begin as a Timer. A separate command stops the Timer App but the phone’s main clock is always running. It never stops. It’s a reference.

The MOXF Clock is always running. The Arp is like the Timer app, it references the main clock, but has its own method of starting and stopping and a separate set of rules about how it behaves.

When the MOXF is the slave, it still controls the MOXF’s Arps, Tempo driven Effects, and the Tempo Sync’d LFOs
Hope that helps.

That explains so much!
Thanks again for your endless expertise.