How many businesses are in the local pack? Three, shown with a map. A link under them opens a longer list of businesses, so a business outside the three can still be found by people who click through. Ads can appear on the same page; they're labeled as sponsored and don't change which three unpaid businesses Google picks.
Why do I show up near my shop but not across town? Distance. Google weighs how far each business is from the person searching, and when someone doesn't share a location, "Google uses what it knows about their location." Closer competitors have an edge there. You compete further out with relevance and prominence: pages about your work in those towns and reviews from customers there.
Does a "near me" search change the local pack? Google weighs distance from the searcher on local searches, and if someone doesn't share a location, it "uses what it knows about their location." The wording still matters for relevance: "plumber near me," "emergency plumber" and "plumber Tampa" are different searches and can show different businesses. Check the searches your customers actually use.
Can I pay to be in the local pack? Not in the unpaid three. Google says "There's no way to request or pay for a better local ranking on Google." You can pay for Google ads, including Local Services Ads, that appear on the same page. Those are ads, labeled as such, and they don't change the unpaid ranking.
How often does the local pack change? It can change with every search, because it depends on the searcher's location and wording. Over weeks, it can shift as businesses add reviews, change their profiles or open nearby. Google doesn't publish an update schedule. Comparing the same searches from the same points each month is the fair way to see a trend.