Prevention is most of the solution.
Get the basic problem information and the model number over the phone from the customer, then set the service time a couple of hours out so you can research the possible issues and resolutions ahead of time.
If it sounds like a doozy and it’s not an emergency, try to set the service call up for the next day to give yourself plenty of time.
If you can narrow it down to a short list of likely sources for the problem, you can study those more in-depth and check them first when you get on site.
Google the model number to find a manual online if possible, and go to a good parts supplier like PartSelect that has explosion diagrams of the appliance components. Check online repair forums, your training materials, and repair books to find those specific types of cases.
By the time you get on site, you should have a pretty good idea of what you’re looking for, so you can confirm it relatively quickly.
But you still may get a curveball, or it may just turn into a difficult repair.
If they are not already aware, mention to the customer that you have a flat rate so they don’t feel the meter is running while you’re working on the problem. Tell them you charge a flat rate so you can be thorough and check everything carefully.
If you just can’t get it done, you can say you ran into some complications, go back and do some more research, get a night’s sleep and try again the next day. Most people are nice and understanding and will be patient. Remember, the worst that could happen if you don’t get repeat business from the customer.
At the end of the day, you probably know more than you think after all your training, and can probably solve the problem in a reasonable amount of time.