Rule #1: Click means treat. If you click, always offer a treat. Even if they don't accept it, you must offer it to keep the effectiveness of the click. If you mistakenly click at the wrong time, you still offer the treat. That is your mistake, not theirs.
In clicker training, the reason it works is that the animal gets paid for doing a behavior you want from them. It is an especially powerful method for animals like the alpaca that are instinctively skittish. They aren't known for wanting to be near or engage much with humans but with clicker training, you can earn their trust and have fun doing so. Once I have an alpaca eating out of my hand, I can usually get them to do all sorts of behaviors. They can quickly learn to stick their noses into their halters with me simply holding it up in the air. While training a batch of weanlings, they so enjoy the halter game that two or three are sticking their noses through the halter at the same time!
The reason the click works is that you have created the Pavlovian response that the noise means something tasty is about to happen. They will want that noise to repeat and figure out what they did that got the click to happen. I'm sometimes asked why a person has to keep giving treats. They want the animal to do the behavior because they told them to do it. My response is, "When you go to work, would you be ok not being paid?" Sometimes we do lots of jobs because we need a paycheck. Well we are asking our alpacas to do something that is really pretty huge. We are asking them to go against their instincts. So it seems pretty reasonable that we should be willing to pay or reward them for doing so. The "cost" to us is minimal considering the payoff.
Whether you have a clicker, use your tongue or use no tool. Reward your alpacas for good behaviors and you will be rewarded with animals easier to handle, more social, save time and energy and you get to have a lot of fun too.