Each question to the site needs to stand on its own and fall into the scope of questions for pets.se There are a range of good and bad ways to ask a question.

With your help, we're working together to build a library of detailed answers to every question about pets. Welcome to Pets Stack Exchange

It is true that story identification questions do well and are popular on SciFi.se there was a discussion about continuing or stopping them and they still remain as about 25% of the questions on the site. We can infer that on that site they add value to many users as well as accounting for a large part of the traffic to the site. Some sites like The Great Outdoors also allow questions about finding specific books I think questions about specific books will probably work well here also.

For the most part new traffic is brought to the site, by search engines (i.e. Google). Having quality questions and answers that people are searching for adds value to the site.

Currently our stats are showing 11,754 visits per day, but only 2.6 questions per day, other wise doing well. While an increase in new questions would be good, they need to be good questions.

In chat Trond suggested some question might do well a special harness ...foldable food bowl for hiking. I tend to agree, special purpose products that are not easy to identify or find, we are probably the best option. If google can't help you find, and others will likely need it, we should try to help.

I tried to imagine a question about a general pet product that people might ask about, and if pets.se would be superior to google for finding.

I saw a person using this purple rubber pet brush and it was really effective for pet hair; what is it?

So we give google a chance to find it Google; purple rubber pet brush and google takes you to it no problem.

Others like the example Does anyone know what brand of dog toy this yellow, miniature, plush, duck toy is? for general products (toys, bowls, bedding, etc) where there are a multitude of similar products that will meet the need, there seems little value to the site to ask about specifics here.

In both of these examples, multiple essentially identical options are returned by search engines. There is no reason to expect anyone else to invest more effort and/or expertise, then the OP to find it.

TL:DR I don't see any reason to ban the class of questions about product identification. But they should be good questions where a search engine does not produce results AND it is reasonable to expect the question and answer will add value to other (not all) members of the community and/or visitors to the site.

Each question to the site needs to stand on its own and fall into the scope of questions for Pets SE. There are a range of good and bad ways to ask a question.

With your help, we're working together to build a library of detailed answers to every question about pets. Welcome to Pets Stack Exchange

It is true that story identification questions do well and are popular on SciFi SE; there was a discussion about continuing or stopping them and they still remain as about 25% of the questions on the site. We can infer that on that site they add value to many users, as well as accounting for a large part of the traffic to the site. Some sites, like The Great Outdoors, also allow questions about finding specific books. I think questions about specific books will probably work well here also.

For the most part, new traffic is brought to the site by search engines (i.e. Google). Having quality questions and answers that people are searching for adds value to the site.

Currently, our stats are showing 11,754 visits per day, but only 2.6 questions per day, otherwise doing well. While an increase in new questions would be good, they need to be good questions.

In chat, Trond suggested some question might do well: a special harness ...foldable food bowl for hiking. I tend to agree, special purpose products that are not easy to identify or find, we are probably the best option. If Google can't help you find, and others will likely need it, we should try to help.

I tried to imagine a question about a general pet product that people might ask about, and if Pets SE would be superior to Google for finding.

I saw a person using this purple rubber pet brush and it was really effective for pet hair; what is it?

So we give Google a chance to find it Google; purple rubber pet brush and Google takes you to it, no problem.

Others, like the example Does anyone know what brand of dog toy this yellow, miniature, plush, duck toy is? for general products (toys, bowls, bedding, etc.) where there are a multitude of similar products that will meet the need, there seems little value to the site to ask about specifics here.

In both of these examples, multiple essentially identical options are returned by search engines. There is no reason to expect anyone else to invest more effort and/or expertise, then the OP to find it.

TL:DR 
I don't see any reason to ban the class of questions about product identification. But they should be good questions where a search engine does not produce results AND it is reasonable to expect the question and answer will add value to other (not all) members of the community and/or visitors to the site.