Choose one long, vigorous shoot that attaches directly to the grapevine trunk on each lateral arm that is tied to the trellis. Cut each shoot back so only 12 buds remain. Make the cut with a bypass/hand pruners. Count the buds from the trunk end of the shoot outward to the shoot's tip. Make the pruning cut 1/2 inch beyond the 12th bud.
Tie each 12-bud-long lateral shoot to the trellis support structure with twine. Tie the twine around the shoot and trellis snugly to hold the shoot firmly, but do not make it so tight that there is no wiggle room and no space for the shoot to increase in size over the summer growing season.
Select another shoot near the base of each newly pruned and tied lateral shoot on the trellis. Cut this shoot back so only two buds remain. This two-bud shoot is known as the spur and provides the long shoots for next year's cane pruning event. In other words, the spur yields the later shoots that will be cut back to 12 buds and two buds.
Remove all other vine branches from the Thompson Seedless grapevine that are neither the newly pruned 12-bud-long shoots or the two-bud-long spurs. Make pruning cuts 1/4 to 1/2 inch above the point where the unwanted shoots attach. The unwanted branches include those that produced fruit the previous fall.