I agree with Chameleonking. Likely your humidity is too low at night (or whenever you spike your humidity levels) that it isn't enough for him to become hydrated.
Also, it doesn't rain every day where our chameleons come from. It actually hardly rains at all. For veiled chameleons, most nights get up to 75%+ humidity every night (ranging closer to 100%). This is how they rehydrate in the wild. But when it does rain, they are hardwired to drink. They are programmed to take advantage of this scarce resource. So when you drip water on a chameleon's face for long enough, they will eventually drink, regardless of hydration. Rain isn't a steady drip of water directly on their face. Raindrops are spaced out and rarely land in the exact same spot, with many drops landing on plant leaves to be lapped up by the chameleon. If you have a dripper that drips too fast, it won't give your cham enough time to breathe. Additionally, it triggers your chameleon to continually drink.
The solution? Increase nighttime humidity and have a good misting first thing in the morning (as well as through the night) to make sure your cham gets sufficient hydration. Also makes sure you have lots of plants for the mist to collect and drip onto. If you want to keep the dripper, make sure there is a long "one Mississippi, two Mississippi," etc between each drip. Aim for 75%+ humidity every night.
I once held a dripper up to my cham's mouth. He kept drinking and drinking and drinking. The continual water drops created a loophole in his behavior. Eventually, he aspirated air. His eyes sunk in super deep and pointed his nose straight towards the ceiling. I swear I was going to lose him right then and there. For some reason, I felt the urge to flip him upside down (completely vertical with his nose down) in hopes of getting the water to pour back out of his lungs. Thankfully, this worked and the water came out! If I left him be and took him straight to the vet, I think he would have passed. The vet was also incredibly stressful for my little guy. It's not worth risking your cham aspirating water. Also, you are increasing your chances of a respiratory infection.