Ok. GREAT. Pics SO say 1000 words.
I *assumed* you had a 3 way diverter but with individual valves the problem is no longer a problem. One blue circle valve goes to the main drain and the other to the skimmer(s)

The skimmer valve isn't closing fully, like a typical ball valve failure, and once the water was below the skimmer, the pump was sucking air through the skimmer leg, causing it to lose prime. Had the pipe and/or the skimmer been the issue (air leak), closing the skimmer valve would have stopped the leak. But it didn't help so that proves the leak to the valve itself. You worked around that by plugging the skimmer and the pump was able to continue draining.
Long story short, the main drain valve hopefully works fine and will airlock the drain leg of the plumbing. The disclaimer being that they are of the same age, and you're likely lucky to have gotten this far with ball valves. Put replacing them with a 3 way diverter, or individual diverters on your project list because the main drain valve is on borrowed time.
I *assumed* you had a 3 way diverter but with individual valves the problem is no longer a problem. One blue circle valve goes to the main drain and the other to the skimmer(s)

The skimmer valve isn't closing fully, like a typical ball valve failure, and once the water was below the skimmer, the pump was sucking air through the skimmer leg, causing it to lose prime. Had the pipe and/or the skimmer been the issue (air leak), closing the skimmer valve would have stopped the leak. But it didn't help so that proves the leak to the valve itself. You worked around that by plugging the skimmer and the pump was able to continue draining.
Long story short, the main drain valve hopefully works fine and will airlock the drain leg of the plumbing. The disclaimer being that they are of the same age, and you're likely lucky to have gotten this far with ball valves. Put replacing them with a 3 way diverter, or individual diverters on your project list because the main drain valve is on borrowed time.