How much suction is needed for it to work?
Not a whole lot. I can't recall if I can move a dashpot by sucking on a hose or not. Why worry about about oxygen deprivation when the engine is a great vacuum source and needs to be tested anyway.
The best way to test is to buy about 8 feet of appropriately sized hose. Run hose from vacuum tap directly to each dashpot. Once dashpots have been tested, it's time to check individual lines.
IIRC, the vacuum hoses through the firewall go from the engine to the harmonica, the other from the harmonica to the hot water supply valve under the hood. The line from the engine to the harmonica, I think, has a Tee that connects to the vacuum accumulator/amplifier.
Since the hose from the engine to the harmonica is the most critical, test it first. No vacuum to harmonica, nothing else works. Start engine, disconnect hose at harmonica. There should be suction at all times on this hose at all times. The line to the accumulator/amplifier should also have full-time vacuum. Get these working properly first. The hot water valve line should only have suction when the A/C is selected.
I don't recall much about where the lines off the harmonica are supposed to go, so check them one at a time assuming each is connected to the correct door dashpot. After all have been tested, cut up the test hose to replace bad lines, if any.