How can I research a brand's sponsorship strategy before approaching them?

Look at their social media feeds, website, which events they attend, and where their ads appear. If a brand is at Loretta Lynn's or a SCORE race, they're there for strategic reasons - understand what those might be. Eric Morley gave the example of seeing Optima's LinkedIn posts about their new power sports battery and recognizing that meant they were targeting power sports athletes. Position yourself to be part of the world they're strategically pursuing. The brands' activities are transparent if you pay attention.