Yes, it is the brake booster.There should be a bleeder valve on it too.
The vacuum lines do develop holes and or cracks in them with time and age.Are the lines hooked up?

There is enough good in the worst of us and enough bad in the best of us that it does not behoove any of us to criticize the rest of us.
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Be yourself. If you are ever lost, It will be much easier to find yourself if you know who you are!