I've tried various thymes in a spot like that and found them difficult. Same with low growing sedums. I finally hit on a winner with Smooth Rupturewort (Herniaria glabra)
- evergreen, drought tolerant, takes some foot traffic, stays low but also spreads out quite quickly. It doesn't get much in the way of flowers, I think some rather inconspicuous greenish ones in the fall. Also easy to propogate, I've been just pulling hanks out and jamming them where I want more. I have mine in full and part sun, plan to try some in deeper shade to see how they do.