Having a command of thirds will not only improve your facility with single note playing, it will help both your ear and your fingers to navigate chord tones. Before you begin playing thirds, play scale pattern #1 a few times. Be sure you have a clear mental picture of the pattern!
Begin by playing tonic (scale degree 1) on the sixth string, followed by scale degree 3 (fifth string). Notice that you skipped the second note in the scale pattern. You will now play the note you skipped (scale degree 2), followed by scale degree 4. You may see a pattern emerging, which will be (by scale degrees): 1-3; 2-4; 3-5; 4-6; 5-7; 6-8 (or 1); 8 (or 1)-9 (or 2); 8 (or 1).
When you have reached the highest note in the pattern, reverse the direction and play descending thirds.
The example shown is in the key of C, using scale pattern #1, but just as you can play any major scale using that scale pattern, you can use it to play thirds in any key. As you add new scale patterns to your toolbox, use the same method to play thirds within those patterns.