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Issue 1 : I go to to https://signin.ebay.com/ws/eBayISAPI.dll?SignIn&runame=<myRuName>&SessID=<SESSION_ID>, I enter my eBay username and password at the first (Authentication) page. However, after hitting "Sign in" instead of proceeding to the "I agree" page (Authorization) I'm logged out of eBay.
Issue 2 : During the Auth & Auth process, after signing in, eBay wants to confirm my identity before continuing. Why is that?
Issue 1 may indicate a problem with browser cookies. Please clear browser cookies and sign in again, or try a different browser or even a different computer.
Issue 2 may arise if you are working from a computer or device which is "unknown" to eBay. This may happen, for example, if you're using a public computer at a library or hotel. For your security, eBay requests identity confirmation before proceeding to token creation. We suggest you to opt in eBay 2 step verification method and add a trusted device to prevent unauthorized access to your account.
REF: Tips for keeping your eBay account secure -> Add 2 step verification