The question How to contact eBay not by the phone has a short answer no way.
If only 3 or 4 years ago you could easily contact eBay support by writing an email, filling a webform or activating online chat, and even could get some answers, no the only way the provide contact is by phone. And the service doesn’t even run 24 hours a day – people overseas may have trouble contacting them.
Even if you place a call and manage to articulate your concern in a foreign language, it doesn’t mean you will actually get any help. eBay is too cheap to hire decent tech support and pay for their services, so they hired some weird morons who just repeat their scripts of common answers to general questions like parrots. You could get the same information by just browsing the answer center.
Even if you use one of the old links and fill in the contact us web form, you’ll receive an automated message asking you to call them on the phone.
All this tells only one sad thing: eBay stopped caring about their customers long time ago. With the ever increasing customer base, why bother? eBay can always replace the infuriated customers with new ones.
So if you have a problem, your best shot is the community forums. But if you have a specific problem, requiring specific actions from eBay, you’re probably out of luck.