I was under the impression that Mozilla also got a sizable chunk of revenue from Amazon. Every time I search Amazon, I do it via the browser search box, and there's a referral code appended. Even if Mozilla doesn't have a special agreement with Amazon (this would not surprise me), they would no doubt qualify for Amazon's highest volume-based advertising rate, which is 8.5% on all sales (excluding electronics and gift cards, which have a rate of 4% regardless of your referral-volume tier).
I presume that the same is also true of eBay in some fashion.
You may want to look into this -- it might be another add-on or toolbar you have installed, since Mozilla does not do that. (Disclaimer: Mozilla employee)
I always found it easier to type "ctrl/cmd-l amazon.com" and do my search than use the mouse to switch engines (is there a keyboard shortcut??) But, knowing that it can potentially benefit Mozilla, I will start using it more often now. Thanks.
I recently found out a life-changing tip with Firefox. Right click any search box on any website and hit "Add keyword for this search." You can then assign a prefix which you can use in the address bar to search that site. For example, I have these set up:
Opera has had this feature forever, since around 2001. Long enough ago that it shipped with search keys for Altavista and Lycos along with Google. The feature was a primary reason I started using Opera in the first place.
Originally you had to dive into a config file to add non-default search providers, but it's now in the UI just like Firefox, right click any text field and select "Create Search".
I presume that the same is also true of eBay in some fashion.