So, you would need a good check-valve on each panel.
Once your vacuum pump came on and got the pump lines down to a low pressure,
the check-valves on panels that had leaked down a bit,
would open due to less pressure in the pump line.
Once the pump turned off, the 14 PSI would hold the check-valves closed.
Check Ebay for "vacuum check valve", maybe an automotive type would work?
Hey, one could set up an un-used HVAC vac pump, on a timer?
Let it run for 10 minutes a day?
