The 2nd lake was looking quite dry in late June
That wasn't my impression. I was there the same day as you, and it looked the same as it has the other two times I've been up to Shepherd Pass. I think it is a year-round water source, and I agree that it is better than the second lake.
Other places to camp on the approach hike in are at Mahogany Flat and Anvil Camp. Anvil seems to be especially nice because is about 2 miles from the top of the pass (2 miles in) and there are quite a few sites and a nice stream to get water from. Also, the first lake at the pass is generally prefered because it offers some protection from the wind and it's really unnecessary to gain the extra 200+' up to the next lake. The 2nd lake was looking quite dry in late June so I wouldn't count on it being a reliable source for water later in the year.
Just a wee question on the name of that mountain. If it was named after the same John Tyndall, the scientist who's name was borrowed for our national scientifc research institute where I work (www.tyndall.ie), then the guy was Irish, not English!! More details on him can be found here: http://www.tyndall.ie/contact/tyndall.html
Only bothered seeing as the name is very familiar to me :)
A flash flood last summer (2013) washed out a section of the Shepherd Pass trail at approximately 10,000', just below Anvil Camp. It is necessary to hike approximately 100 feet upslope from the trail to cross near a large rockfall. There is a second washout a little higher as well, but is easily bypassed and is cairned.
There are no longer restrictions on when you can visit the area. The trail has been rebuilt to get around the big washout below Anvil Camp.
Attempted to climb Mt Tyndall on 4/10/2019 from Shepherds Pass Trailhead. We abandoned at 10,000 feet. We were the only ones at the trailhead for two days.
Conditions: weather was clear with some 25-40 mph wind gusts. Deep snow starts at about 7300 ft., at about the 15th switchback, one hour in (there are about 55 switchbacks in the first phase of the mountain).
The climbing grade was about 100-115%, which made the first part brutal. If you start early in the morning you can use crampons, but by 1 pm you're going to need snowshoes with a heel lift otherwise your feet will sink in to about your calves and thighs at times (very very frustrating). You will also need short trekking poles and actual snow boots (not waterproof hiking boots, snow boots).
Where there are usually streams to replenish your water supply, there are none after 10000 ft (not that we saw), which means you have to melt snow for water.
The grade was too aggressive and demanded more than we were willing to give for the first day and decided to call it at about 10,000 ft. We went elsewhere and climbed smaller peaks.
What I learned: The importance of having a heel lift on proper snowshoes will make your life a lot easier. My calves were smoked after the first four hours of climbing straight up with a 45lb pack.
Recommendation: Unless you have 4 days to give the climb and you're in extremely good physical condition I would recommend waiting until the snow melts to about Anvil Camp (maybe late May). It can definitely be done and it's absolutely beautiful up there, but I would leave this one to the more experienced.