Bendix brake booster troubleshooting?

Greetings All, I am new to the community but cut my teeth on ‘60’s Fords and Mercurys. I am helping a friend with a 67 Mustang to diagnose his power brakes. I know there are other forums for this but after lurking for a while, this one seems solid. I need a sanity check before I spend my friend’s money.
Symptom: Extreme brake pressure to stop.
Tests:
1). Confirmed that the pedal doesn’t drop at all when the engine is started.
2). Confirmed that the diaphragm holds vacuum for an extended period- like an hour or more.
3). This is the one where I think I see a problem: There is continuous flow of air through the booster when the brake pedal is depressed. I expect the vacuum valve to close when the atmospheric valve is opened by depressing the pedal so that you don’t get a huge vacuum leak when holding the brakes on.
Am I wrong in this?
A little more information- as noted in the title, the booster says Bendix, so I guess it’s from a ‘69. It has a 4 wheel disc conversion but equal volume reservoir master cylinder that actually look like it came off a car with 4 wheel drums originally, though it has port size adapters so maybe not.
It also has the fuel injection system off an ‘87 5.0. As another test, I pulled the vacuum line off the IACV and plugged it with a vacuum gauge, and the engine loped until I pushed on the brakes then smoothed out, so definitely getting significant air through the booster.
Thoughts?
Any other ideas for troubleshooting before I make the call?
Apologies if this has all been covered before on the forum, but I didn’t see it in my search.
Thanks!

A ‘67 should have a Midland booster which is much more responsive than a Bendix. A booster is bad if it does not respond to vacuum, further evidence is a big vacuum leak. You can cap off the vacuum to test that. I would search for a Midland core and have it rebuilt at Booster Exchange in Seattle WA.

Thanks Royce!