Hey, I'm a PhD in [field] and do [whatever] professionally. Before calling you, I've narrowed down the problem to [something on their end], so that's what needs to be addressed. If I could speak to an engineer about [specific problem], that'd be great; but if we've gotta walk through the script, let's just knock it out quickly. If they end up requiring the script, then the best way to use your expertise is to run through it quickly. Keep the chit-chat to a minimum and just do the stuff efficiently. If they start describing how to perform some step, you might interrupt them with, "Got it, just a sec.", then let them know once you're ready for the next step.

So what can you do to demonstrate your technical knowledge? Well, you are doing the right thing by using the correct technical terms. That will give an indication to the person handling the ticket. Explicitly explaining your role as the administrator or developer should also help.

From experience I can say that professionals will be more forgiving if you go through things at a basic level than amateurs who have no idea what you're talking about, so people will probably err on the side of caution and not assume the customer has a high level of expertise.