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The "black ball" is the vacuum reservoir, it holds vacuum for the Vents in the cab, Floor, Panel, Defrost, these use vacuum "motors" to open and close
Odd that its not on the diagram, VAC RES
Just FYI, it has a black line that runs to the firewall and thru the firewall to the "Climate" control panel
This line can crack or melt(exhaust pipe), and you will only have Defrost vent in the cab, that's the default "no vacuum" position for the vent doors
And there is a Grey vacuum line that comes out of the firewall at the same location that runs to the Heater hose By-pass valve, this only has vacuum when MAX AC is selected, it closes that valve so no HOT coolant is circulated in the heater core, so max cooling for cab area
Yes I do see the vacuum hoses going the firewall into the cab.
Funny thing, during the recent smog check, the tech questioned this clear vacuum gauge line. He thought I was an undercover DMV investigator trying to trick him into giving a "Pass" for a modified smog system. Once I explained what the vacuum line was for a gauge and then showed him my business card that I was not a undercover DMV agent - he was relieved. The good news is the truck passed the smog test with no issues.