This ended up being a much longer process than I anticipated. I applied online, then was sent a personality assessment a couple days later. I completed that and about week later they sent me a critical reading test and a spatial reasoning test. Both were timed and somewhat challenging, especially the latter. About a week after that, I received an email to set up a time for the phone interview. That took about 30 minutes and was pretty straightforward; the interviewer asked the regular questions (strengths/weaknesses, leadership examples, etc.) plus put forward some hypothetical situations mostly relating to time management. At the end of the interview he told me he was approving me for the next stage, an in-person interview of sorts.
That took place 2 weeks later at a Geico Express in Alexandria, VA. They sat me in an office where I listened to a 30 minute recording of instructions for a simulation. I was expecting the material to be automotive-related, but instead I was to pretend to be an insurance adjust for a company that handles warranties on medical storage, generators, phone switchboards, and other apparently random equipment. They also provided me with a written copy of the instructions, charts, maps, pens, and paper. The simulation itself was very challenging. I had to react in real-time to "customers" and "repairmen" over the phone and in person, using the paperwork I had been given. The names, different companies, and the repairs were pretty confusing and I got flustered a few times. One of the men running the simulation also pretended to be a rude repairman to see how I would respond to antagonism under pressure. The entire thing took almost 2 hours, and I wasn't at all sure what my results would be.
About a week later, they called me with some follow-up questions, my opinion on the simulation, and to offer me the job. Then came the background check, credit check, and hair follicle drug screen. That took about 3 weeks and I was getting nervous because I was running out of time to put in my 2 weeks notice before the training starts. Happily, everything has been cleared and I will start training next week.