A quickie test for most common C6 no/late/soft shifting problems; Check da Vacuum Modulator and its Vacuum Line; it's at the back of the transmission.
also:
"...The different color bands indicate the diameter of the rubber diaphragm inside the modulator. The two COMMON colors from auto parts suppliers are PURPLE and GREEN. These are for CARS. TRUCKS like OURS REQUIRE the BLACK banded modulator, likely from a transmission shop or dealer. This is reguarding the mid/late 80's models, maybe more... Id venture to say any C6 with a slip in modulator. Again, PURPLE and GREEN are NOT the correct units to use, BLACK is the intended modulator as was designed for TRUCKS..."
Source: by MyFullSize (Andrew)
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Trouble Shooting Flow Chart
Source: by jasperengines.com via web.archive.org
"LATE OR NO SHIFT
Check vacuum to modulator - needs 18""
Check kickdown cable or switch
Stuck or dragging governor
Valve body..."
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Ck shift linkage
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an Overview of the VM/kick down, etc by JGVABronco78