I think the other answers make it clear what's going on, but I wanted to add some more details. That red cap is probably not meant to be water tight, so when the water level in the pan is high, it will drip.
What is common in my area is that there is a "main" drain line, usually plumbed with PVC pipe (not that flext tubing you have) that will drain condensate into a drain pipe in the house somewhere. The second drain hole will be plumbed to a "backup" drain that will drip in a safe, but obvious place. It might drip out of the eaves of the house or onto the driveway, etc. The point is when you see that dripping, you know the main drain is clogged.
In cases where a secondary drain is not feasible or to make sure a leak never gets out of control, an A/C tech can install a float valve on the second drain hole that will cut power to the unit when the first drain gets clogged. The drain water backs up into the second hole and trips the float valve. If the A/C can't run, it can't generate condensate and leak. You're forced to fix the drain problem rather than ignoring a drip from the secondary drain.
Anyway, my recommendation would be to make sure that primary drain is going where it is supposed to. It really should be re-done properly with PVC. Also, installing a float valve is pretty important in your case because an overflow in the pan is going to drip water all over your furnace, possibly causing some expensive damage.