what's your process for finding low competition keywords?

Look for results where the page ranking doesn't really answer the query - an old forum thread, a product page sitting on a how-to question. A mismatch like that tells you more than any score.

On an inherited site I would spend the first hour in Search Console rather than a keyword tool, because whatever the site already gets impressions for is your shortlist and it costs nothing. After that the order I use is: write the query down, open the real results in an incognito window, and look at who is on page one. If it is eight national brands and a comparison site, the difficulty number is irrelevant, you are not getting in. If there are a couple of thin blogs, a forum thread and an old PDF sitting there, that is a low competition keyword whatever the tool says.