One of the most challenging checkering jobs you'll likely encounter is round knob grips. The changing contours cause all those lines to go in unexpected directions. If you aren't careful, your lines will bend wrong and your diamonds will change proportions as the coverage flows over the lower portion of the knob.
The trick is to start your checkering across the top of the middle of the round portion of the grip. Both master lines should cross about at the crest / high spot on the knob.
The best way to handle it is to lay out your master lines in the usual way, which with the way I always do it is to place them up towards the top, where the lines will be longest. By doing it this way you can control the angles of the points, placing them where they will be the most pleasing visually.
You won't actually use those master lines. Lay a strip of Scotch® brand Magic™ Tape along your top master line, building construction master lines as you work toward the right place to start. When you've laid enough strips to arrive at the correct place to make the new maser lines, lay out the other side of the grip to ensure that both panels will match. When you're pleased with the entire layout, cut in master lines in the new places and make knife cuts along the edges of all your layout tape except for your original master lines up on top. Just mark that one with yellow pencil, or leave the tape there for now. This is because if you miss with your layout, you might have made a knife cut in the area outside of your checkering panel.
Now lay Scotch tape down over the construciton lines you've cut, centering the tape over each line. Cut along the edges again, and you've got guide lines every 3/8".
Since your lines will want to go off track at the ends where they meet the outline of the panel, I'd suggest you cut two or three lines at a time, stopping a bit short of the ends. You can then inspect the ends and finish them with your 60 degree veiner, making sure they terminate at the right place and at the right angle, each and every one of them.
I know this will be tedious, but those lines will be there for a long time. Make them right.