Doug, I reread your post...
You can actually install an automatic transfer switch.
An automatic transfer switch can accept two sources of power...and default to the priority source when available...or secondary source when the primary is not present.
They make these for solar Installations so that the solar powers during the day, but utility would power at night.
Making the power from an add-on inlet box which will be connected to your external generator, could be wired as the primary. Then run the power from your second a/c's breaker to the other auto transfer switch input. Wire the output of the ats back to the wire going to the a/c unit.
Once wired...that air conditioner would function from thee source it normally uses. If you see a need to run the generator...start your normal generator...but only turn on the #1 a/c unit for the time being. Then hook up your external generator to it's inlet box and start it up. When the ats sees power...it will switch the #2 A/C to the external generator, as it has priority if present. Finally, turn on the second A/C. Just know that if the external generator quits...both a/cs will be back to trying to run on the onboard generator.
Does that make sense?
It's a specific work around for the #2 air conditioner only...
You can do it even cheaper with a manual transfer switch. It would be wired the same...but you manually select 1 or 2 for your power sources.. they usually have a 0 position as well, which removes power from the A/C. These are only like $12 on Amazon...and since you have to manually hook up the external generator...a manual transfer switch wouldn't be that much effort to set for the desired source.
I have done something similar...but I am manually selecting main AC power or Inverter power to run my front A/C unit. It's a Leviton 20A rated dpdt switch. This allows switching the neutral along with the line from the selected source of power.