The tarns are my favorite jumping off point to climb Whitney from the backside. I would say that I have climbed Whitney two dozen times using this location.
There are rock walled campsites, and the views are tremendous, especially at sunset.
Normally, from the tarns, I am at the junction of the trail from the east side in an hour and half.
When I camp there, I leave around 3 to 3:30am and reach the junction by 5am and the top by 7am...... from there I hike out the same day, meaning I reach the trailhead around 2pm or earlier.
I know the point of this is that yes, water can be an issue. What I tell people, and I have done this in dry years, is that I have dinner at Guitar, or the small pond just beyond Guitar, and fill up all my water bottles and hydration bladder and head for the tarns after a nice dinner and set up camp.
It's nice to get the 1/2 to 3/4 of a mile out of the way. And it puts you closer to your destination.
Guitar can be crowded (not like Trail camp crowded). Also, depending on where you camp at Guitar, hikers are usually up by 2am and start leaving by 3 to 4 am.
I always find it fun to get on the trail by the tarns, and look back to a long line of headlamps coming up the trail behind me.
paul