Here's somethings to help you on Twitter, Tim.

Getting engagement increases impressions.

Start replying to all comments on your tweets. Your engagement will go up. You have a large enough following, people would freak out to get a response from you.

Second, take the time and engage on other people's content you're interested in. You will see an increase in followers which will lead to more engagement.

For everyone else who doesn't have a large following.

Engage on other people's tweets a lot (25-50 different tweets everyday). People won't find you searching. They'll find you being a part of a community.