Does anyone have tips for securing customer interviews when your customers are relatively unengaged very small businesses?

I've had a similar scenario in the past. What worked best was to first automate the requests for interviews so you are not spending a bunch of time emailing or calling customers you aren't sure will be interested in speaking with you. We did this in the form of a win/loss email request a couple of weeks after an opp was closed in Salesforce. We also offered a "small token of our appreciation" -- a gift card of a small amount.

I'm curious to see what has worked for others. More recently my challenge has been getting the right person in the organization on the phone (someone who was invovled in the sales process/the decision maker).

That can be a tricky situation! Essentially, you need to develop your customer engagement in order to develop your customer engagement :-) Classic catch-22. I have been in this situation in my work at smaller companies and have found a couple things that work well -  

1. Adopt the mindset of "quality over quantity." It is fine that you don't have dozens or hundreds of customers to talk to - you only need a handful for interviews anyway. Don't worry about the numbers.
2. Pick out 5 names from a customer list who have had a memorable sale, testimonial, recent meeting, or other transaction with your company, and contact them directly with a highly personalized message. If you can only find 1, 2, or 3 customers, that's fine. Start with that! If needed, spend 10-15 min with the Account Manager or Sales person to understand a bit about that customer so that you can tailor a message for them. On blanket emails sent out to large groups of customers to participate in interviews, I have found that a 5-10% response rate is about as high as you're going to get. But on the personalized emails where I reach out to people directly, response rate is very nearly 100%.
3. Be humble and human. You are contacting your customers because you want to improve your product or your business. Be upfront with them about this, and don't sound like a robot when you write your email to them. Make sure you sound like an empathetic human being who genuinely cares about their business and their experience with your product. Don't be afraid to use a bit of humor to loosen the vibe.

Good luck!! 

Are you in a (budgetary) position to offer some kind of incentive? Not sure whether your demographic would respond to this or not, though.

Otherwise, my #1 suggestion would be: make it as easy for them to say 'yes' as possible!!!! Lose the video conference. Skip the meeting invite apps. Meet them where they are.

They're only at a desk an hour a day, but commuting in their cars for two? Make it a phone call.

They've never seen Calendly before? Don't be the one to introduce them to it. 

This is actually a good exercise in becoming more customer-centric, as it is an opportunity to figure out how to connect with your customer base to solicit (and receive) feedback.