I started hiking from the Mono Pass trailhead about 2 miles west of the Tioga Pass entrance on Highway 120 at 6.50am. The trail is even and passes through lush meadows and forests for about 3+ miles till a junction. The right fork is marked to be 1.7 miles to Spillway Lake and the left fork says 1.7 miles to Mono Pass and 3.7 miles to Parker Pass. I took the left fork and about 1.4 miles later is the marker saying "Mono Pass 0.3 miles". Just prior to coming to this marker is a small junction marked by 2 cairns on either side of the trail. A sketchy trail
forks off to the right but gets pretty solid a quarter mile later. Follow this trail that goes over gently ascending terrain till wind swept Parker Pass at 11100 ft marked by 3 trail markers. Continue on the trail as it drops down to a beautiful valley. Through a large gap in the cliffs parts of Mono Lake are visible. At this point the trail veers right and starts climbing the northern flank of Parker Peak via tedious switchbacks. Koip is visible on the right as a huge talus hulk with a permanent snowfield that has a bergschrund on the top. The switchbacks end and the trail traverses till the saddle between Parker and Koip. There is a marker here that says 'Koip Peak Pass'. Koip is a short walkup on the right over some typical Sierra talus.
These were my times in getting to the peak. I was slow. Start: 6.50am. Parker Pass (11100 ft) at 9.20. Summit at 12.30 pm (5hrs 40). Left summit at 1pm. Back to Parker pass at 3 pm. Back to car at 5 pm. Round trip: 10hrs 10 mins, 18 miles.