I’d like to propose Option #3: GA’s dedicated search tracking with Search Category set. This will give you the four reports under Behavior > Site Search and allow you to analyze search behavior as a whole or divided by type.
Note: this setup uses an Advanced Filter, which can’t be verified via preview, so apply it to a testing View before making the changes to your main View.
First, in your View settings, enable Site Search Tracking and set
q as the query parameter.
In the screenshot I haven’t checked “strip query parameters out of URL” but I personally would select that. Also, this step should be fine to do in your main View right off.
For categories, you’ll need a View Filter set up as follows:
You’ll create a new Custom filter of type Advanced, find Request URIs that match your two search URLs, capture the category identifier with
(blog|products), and output it to the field Site Search Category.
Once you have the filter defined and it is working the way you need it to, you can apply it to your main View with the Apply Existing Filter option also shown in the screenshot.