Any advice on how to run customer interviews?

The best advice on that topic I've read is a book "Mom Test" (see my summary at https://blog.kowalczyk.info/dailynotes/note/b4u674cvj43jdajdsukg-summary-of-the-mom-test-book-about-validating-business-ideas).

The idea is that you have an idea for a project and you ask question that would confirm or disapprove the idea.

It's very important: those are not direct questions like "what do you think about idea X".

In your example it seems like you're planning some sort of hiring platform to connect tech employees with employers.

The "Mom Test" of doing this would be to start by asking the employee about his past actions. The conversation might look like:

"How did you get your last job?"
"I was contacted by a recruiter".
"I see. Did you also apply to other jobs at the same time?"
"Oh no, just this one"
"Was that the only recruiter that contacted you?"
"No I get contacted recruiters all the time".
"Why did you respond to that recruiter and not the others?"
"He was from company I was interested in."
or maybe:
"Most recruiters don't even bother to read my resume I have on my website. He knew my background, read my resume so I had confidence that there might be a match with the company he was recruiting for"

You go with the flow of conversation but ask probing question that reveal the answers to questions you might have.

Conversation with a different person could be:
"How did you get your last job?"
"I sent my resume to people".
"I see. How did you find people to send the resume to? Did you find them on a job aggregator like Monster.com? On stackoverflow jobs? Did you apply to the companies through their website?"
"Oh, it was through Who's Hiring thread on HackerNews"

When you have such conversion with several people, you'll notice patterns. Some number uses a recruiter. Some pro-actively find jobs. Some are poached by friends etc. You begin to form an understanding of what people do.

Notice that in Mom Test you rarely ask direct questions because they both prime the people and limit what they might say.

For example, you don't ask "How do you usually find jobs? Recruiters? Linked in? Referrals from friend?"

You can never enumerate the possibilities. You ask "how did you find your current job?"

You also don't ask speculative questions like "what is painful for you" with multiple choice answers.

If e.g. you have a theory that spam from recruiters is a problem for people, you might ask:

"So, how often do recruiters contact you without being asked?"

If they say "I don't know, not that often" then you have an answer (it's not a problem for them).

But maybe they get angry and say "Oh, all the time, I hate that linked in crap".

Then you might follow up with: "So how many times did you get contacted last month?"

If they say "Oh, 3, maybe?"
"So what do you do in that case?"
"I just delete the email".

So that also an indication it's not a problem. They might be angry about it but they have it an easy solution.

Think of it as data points vs. opinions.

"When I was looking for a job last time, I had 2 offers and picked the one with a higher salary even though the other job was closer" is a data point that suggest that this person values salary more than other things.

Getting this data point is better than asking "so, is salary more important to you than other things"? This requires the person to introspect about their values and they might not be truthful (e.g. they don't want to come off as greedy).

It's better to get them to tell you what they did and then infer their values from that.

Of course you have to steer the conversion in a way that will lead the person to revealing data points you care about.

My wife is a professional researcher and has helped me a few times. One of the things she taught me is how useful a guide can be when conducting user research.

You might find this article useful, it's an excerpt from a book on her bookshelf:
http://alistapart.com/article/interviewing-humans

Another vote for the Mom Test book. In general, avoid leading questions, avoid yes/no questions when possible, and focus on trying to get the interviewee to tell stories and share experiences. Dive into their answers with follow-up questions, let the conversation flow naturally. Your script is a starting point, if the convo has momentum in a direction, it's okay to get off course and follow it.

Don't go in looking to prove yourself right or wrong, go in looking to learn and listen to what they have to say.