Google Search
Google Search is probably the first place to start. Search your client. Their website (and maybe socials) will come up first (hopefully) so scroll until you see a different brand.
Search up the type of product that they sell or are known for and check out the top results to show up. Be realistic, though: if your client sells something that seems similar but is at the opposite end of the price spectrum, keep the difference in brand and audience in mind. Send yourself on a mini rabbit-hole wander and jump from site to site. Keep a note of the styles that you see: any patterns, fabrics, colours that they like to push more than other designs.
Facebook
Facebook is, of course, another great place. But not for the reasons you might think of right away. Facebook groups for fellow marketers can be searched for others asking questions about the same type of product your client is trying to sell. Use the search function to look for posts that include a couple of keywords that relate to what you’re selling and, chances are, you’ll find that someone else has asked the same question. You’ll find people looking to sell something to rich, old people or teens who go to music festivals and the comments will typically be full of helpful advice (and memes). This method can be a hit or a miss depending on how niche a product you’re trying to sell but can definitely provide some inspiration, intentional or not.
Facebook Newsfeed
Your Facebook Newsfeed. This piece of advice only really works if you’re part of the target demographic, or close to it. Click the little drop down arrow next to the ad that you’re seeing and click ‘Why am I seeing this?’ It will let you know if you’ve been targeted because of your demographic, interests, or even location. If you’re lucky, it might reveal something about the type of person the ad is targeting. If it seems like you’re the wrong type of person for what they’re selling, make a mental note of that – they’re probably sweeping too wide. If you had even a second of interest in it even when it seemed unrelated, mull on why this was the case. Was the ad super attention-grabbing? Could you see other people in your demographic/with your interests also pausing?