Are there any ranking factors of the core importance that would make Google’s local SEO by definition?

Regarding the very concept of local SEO by definition, all top ranking factors of the core importance for Google itself are falling into just four basic categories. Basically, all of them can be related to General Ranking Factors, Localized Organic Signals, Negative Ranking Factors. And Local Difference-Makers. But before we go any further, it should be noted that this short post is intended just to provide a sufficiently clear response to your question. I mean here that the following explanation is going to cover each locally-targeted factor and every ranking signal without exclusion – everything listed below would have a measurable impact on local SEO, by definition. 

Put simply, while this seemingly extensive set is meant to pull together the whole array of local ranking factors, the following information itself isn’t terribly actionable (at least when considered on its own). Just for the sake of completeness, my intention here is to show you a great multitude of signals used by the major search engines (like Google itself) to determine each page’s final positioning in local search results. All that being said, here is all you need to that point.

What Makes Local SEO by Definition: General Ranking Factors/Signals

• On-Page Signals – can be simplified down to just two key elements, such as Relevance and Authority. And in the eyes of Google's local SEO, by definition it wants to consider the following key on-page elements: Title Tags, Meta Descriptions, Header Tags, Images, Google Map, NAP Data (to be polished with Schema.org Markup), and Body Content itself. As for a bit more specific elements used by the search engines to evaluate Credibility, the strongest priority is commonly delegated to External Reviews, Accreditations, and Testimonials. 
• Link Signals – given that this area is particularly specific to be completely outlined just in general terms, the is no particular categorization rule available over there. Much like with standard SEO, Google's basic approach to local rankings tends to look for Location-Specific & Industry-Specific Links, Authority Hyper-Local Links, and True Editorial Links. 
• Google My Business Dashboard Factors – are commonly related to Correct Categories, Keyword-Based Business Title (of course, when applicable), Searcher's Location Proximity, Interior/Exterior Photos, Call-to-Actions in Business Description, Net Positive User Feedback.
• External Local Signals – this type of ranking factors seems to revolve mainly around NAP Consistency, as well as Citation Volume (i.e., shreds of business NAP data , pulled together from yellow pages-like online resources, as well as big data aggregators, and local listing/business directory submission).

• Review Signals – while they are bearing quite modest ranking benefits, Review-based signals are strongly dependent on their Number, Velocity, and Diversity of the user feedback.
• Social Media Elements – again, much like with general SEO, these signals are well-known to be represented with (but, of course, not limited to) Facebook/Twitter/LinkedIn likes/follows/shares, as well as Google Plus authority, Business Profile Branding/Keyword Saturation, Social Media Activity, and so on.
• Behavioral Signals (otherwise, Mobile Engagement) – are generally related to Click-Through-Rate, Mobile Click-to-Call, Seasonal/Location-Specific Offers, Schema Markup Structured Data, etc.