GEICO is on Twitter and that's great if you are too (we're guessing you are since you're here). Generally, companies respond quickly to customer requests made via Twitter because they know the conversation is public. However, many customer service teams are not equipped to actually solve problems over Twitter and they will often reply quickly to tell you to call or direct you to their help desk. We're not saying that GEICO will do this, but don' be surprised if they do.
One thing you might like even more than trying to tweet or DM GEICO your customer service problem is to use GetHuman's problem-specific help tool. For companies and problems where phone is the best or only way to deal with the issue, we give you tools to get through to a rep as much as 75% faster. But for companies like GEICO that might not have a phone number, we also provide tools for getting their attention on Twitter and linking back to a page that you own on GetHuman's website. The nice thing about that is that you can track views of other customers on your own page, which is something that GEICO's personnel would be able to see as well, meaning that you can share and publicize your issue to get attention faster.
Of the 10 way(s) to get in touch with GEICO, customers like you claim that the best one is the 800-841-3000 option. From this page you can easily access all the possible contact information options for GEICO as well as read up on common problems that other customers are having, find out how to fix the most popular ones, read reviews, and more. Know of any other ways to reach GEICO? Pretty please let GetHuman know about it. We work hard to bring you as much free information and tooling as we can, and we grow that toolset every day, bringing things like the call-back tool that skips the hold music when calling a company or call-recording for customers (beta). The more you use GetHuman and tell friends about it, the more we're able to provide useful, free tools for you and customers worldwide.