In terms of extracting tannins, all you care about is the pH of the runnings. But since gravity and runoff pH are so closely correlated, tracking one means you are also tracking the other. So track whichever is easiest for you to track. If you're adventurous, track both pH and gravity for a few brews, and make a plot of pH vs. gravity. You'll see the close correlation, and this may also help you adjust for variances in your equipment or processes.
All that said, no one I know, me included, bothers tracking runoff pH or gravity. The only way I'd be still running off into the kettle when the gravity is near 1.010 is if I've made a big miscalculation with the recipe.
Iodine complexes with amylose, the main starch in malt. If amylose (i.e. unconverted starch) is present, the sample turns dark-purple/black. You can use this color change to check if conversion is complete or not. I consider this test pretty useless because, as long as you've created reasonably normal mash conditions, full conversion will always happen, I guarantee it.