Hi
While it's impossible to predict exactly what ebay/paypal will do in any situation you are FAR less likely to get banned if you login using the same machine (i.e, using the same cookies) from a different IP. Many people have dynamic IPs and EBay/PP cannot ban someone just based on a changing IP - too many people would get banned.
I try to keep IP address I use to login to ebay constant but I have logged in to 1 ebay account with multiple IPs in the past and did not have an issue bec of this.
That being said it is possible to use a "bad" IP address (i.e, an IP that's been overused / banned on ebay) and it's hard to differentiate the good from the bad. Therefore, when possible it is best to stick to one IP.
I hope this helps.