The first thing to ask would be did they ask you for make model and serial number? This helps with knowing what unit you are talking about and whether or not who you’re talking with repairs that make (brand).
Second, explain the problem that is happening and have them repeat it back to you, this ensures they were listening and documenting prior to answering.
Third is the person taking the call or the technician that calls you easily understood and are you comfortable over phone with them. This one is critical because a phone relationship is easier than in person.
Fourth find out the experience level of the technician: How long have the worked as, how many of your brand have they worked on have they ever seen your model, are they familiar with the problem?