I'm not a pro detailer, but I have done a lot of customer service, some for high end brands. I've dealt with price - sensitive people before, and one thing that tips me off is if they ask a ton of questions, as if they're stalling for time before they come up with an excuse as to why they won't buy something because they don't want to sound cheap. There is a difference though, where in car detailing, you're self employed so it at least is 'possible' to haggle, in a department store, you know you can't haggle, so it's clearly yes or no on the given price.
They seem to get anxious, too. If you can tell when someone is anxious and uncomfortable, you can tell when they're price - sensitive. Some people will even ask if it will go on sale soon, so if they ask if any promotions are coming up, there's a sure sign!