Why when I add garlic to an existing flavor base with veggies, it rarely gets golden brown?
One thing you can do is push the rest of the contents aside and make a little well into which to add your garlic directly onto the bottom of the pan. Give it a little stir (I assume it's crushed or finely chopped) and then mix the other veg back in. If you haven't got room to do this your pan is probably too crowded already.  You may want to add a few drops of oil to this clear spot just before the garlic, up to a teaspoonful.  This would be my preferred approach if the garlic doesn't get much more cooking, e.g. in a stir-fry (which can also tolerate a little more oil).

Another approach is simply lots of of stirring and a nice hot pan - if the other ingredients burn you added the garlic a touch too late.  It can be hard to tell when the garlic gets golden brown this way as it disperses into the rest of the veg, but it works well for slower-cooking dishes.

With onions I've found that recipes frequently imply a much quicker process than in my kitchen, and the same may be true for garlic.  I suspect that the pros use a hotter, heavier, pan, and having everything prepped already keep things from burning by lots of stirring.