Pretty common problem on a 700r4/4l60 trans.
Usually it is the governor.
Governor is located on the drivers side of the trans behind a metal 3 inch diameter cover. The governor cover leaves the factory painted black, but it is usually the rusty thing on the trans by the time we service it. Like an old style wheel bearing cover, a screwdriver and a hammer will tap the cover off allowing the governor to pull right out.
Inspect the governor gear. If it is stripped, broken or apple cored(center ripped out) it will need replacing., Gear kits are available for $10 or so.
Inspect the valve by pointing the governor gear toward the sky and squeezing the weights in and out while watching the valve in the center mover up and down. It should move freely without binding..025 or so is the range of motion. If not, it can be disassembled, cleaned and polished to work well. Be aware though, the gear will need to be removed to do this. The gear typically breaks when disassembled.
A new governor is currently available in the aftermarket and from gm, but I usually recommend fixing the vette trans governor to allow the trans to maintain the factory correct shift points.

Great tip!! Thanks!

excellent tip, thanks for the info

TTT