Cook had eight birdies, two bogeys and a double bogey to reach 8-under 135. He won the 1981 Bing Crosby National Pro-Am at Pebble Beach for the first of his 11 PGA Tour titles.
Kendall, playing in his second Champions Tour event after earning a spot in the field in open qualifying Tuesday, had a 69 at Pebble Beach. Byrum shot a 3-under 68 at Poppy Hills.
The final round will be played at Pebble Beach.
Marco Dawson was fourth at 6 under after a 68 at Poppy Hills.
First-round leader Blaine McCallister was 4 under after a 73 at Pebble Beach.
Two-time defending champion Kirk Triplett was 2 under after a 72 at Pebble Beach.