Don't be fooled by trends, or by your company's current infatuation with any buzzy topic of the moment that happens to play to your strengths. Companies eat up and spit out new trends every quarter. Instead, look to things more fundamental and deeply ingrained: org structures; career tracks (if any) for your function there; the power structure and network of decisionmaking; how the company makes its money; etc.
If tech is not really that important to your company, you've got a choice to make. Stick with the company if you want to coast, and perhaps to reach a nicely compensated sinecure within the firm. You can do well for yourself, but you might never really climb the ladder, or attain strategic importance. There's nothing necessarily wrong with that. That's the endgame perhaps 90% of all workers strive for. Leave if you hunger for something more than that.
On the other hand, it is certainly possible to become a hot, exotic, and indispensable figure at a non-tech company by being a techie who is sufficiently skilled in the arts of politics and influence. But you will need to master those arts. Technical competence alone, even extreme competence, will be necessary but insufficient.
Ultimately it boils down more to people than positions or market. Do management perceive any ideas you have about tech projects that could improve the company's efficiency or sales as a sign you're a rising star or that they haven't given you enough instructions on how you should be spending your time?
You'll have to consider and navigate all of these things. While these are good skills to have in any role, technical or non-technical, they are especially crucial at a company where you're removed from the core line of business. If you're in a technical role at a non-technical company, you need to be an especially strong presenter and "internal salesman" of ideas. Don't assume that because you brought an idea forward, it'll be adopted straight away -- or that when it is adopted, you'll be credited.
I'm not saying this out of cynicism per se. I've seen technical people thrive, and even kick ass, in leadership roles at non-technical companies. At the same time, I know that those people are an exception and not a rule. What tends to make them exceptional are their political skills. Corporate America likes, but does not necessarily reward, a workhorse. But it loves, and handsomely rewards, a "Big Idea" person. It's hard to be the Big Ideas guy unless you can hook your ideas into the KPIs your company cares the most about.
If you're in a smaller company or startup then you've just got to have hustle. Chances are that there are half a dozen unfilled job roles around you and you just need to step in.
Both cases summed up by this advice I received early in my career:
"People don't promote you into a role until you're already doing it."
Being in a non-tech company could be a good thing. It mostly shouldn't be a variable in your situation. You could have the chance to greatly expand the tech work in the company. I personally think all companies need to have a huge emphasis on in-house technology these days. Even if they contract out the bulk of their work, they still need knowledgeable people on staff to be responsible for the consultants. I say this speaking as a freelance consultant myself. I can only do what I'm told. Someone else has to set the policy, and I've seen what happens--on several occasions--when liberal arts majors are made CTOs of companies.
I also firmly believe in not asking for permission to take on responsibility. If you are meeting your expectations for work, on time and on budget, then there is nothing stopping you from being proactive about side projects and anticipating needs within the company.
If, in doing that, you don't receive the recognition you think you deserve, then you will know it's time to find a new company. But just because you're not being given the chance to shine that you think you need to get the promotion you want, isn't related to it being a tech company or not. You won't find a tech company that hands you opportunities.
I worked at one company for a long time (10+ years). There was something about it that really bothered me, and it took me a long time to be able to articulate it.
The way I eventually phrased it: You are what you were hired to be.
I was hired as a junior engineer, and it seemed like no matter how much I learned and how much more I contributed to projects, I was at least partially viewed through the lens of that initial hire as a junior engineer. I had to fight hard for promotions, and like others have said, the commensurate pay only came after I had been operating at that level for some time.
Once you know this, it's not so bad. I'm happy where I am now, and I'm not job hunting. But I know I won't want to do this exact thing forever, and when the time comes for me to make a change, it will very likely be to another company. I tried too long before to find career growth satisfaction with one employer. I gave them too many years to underpay me (it's more than just pay of course, it's the recognition that your value to them has increased).
It sucks to assume that switching jobs will automatically helps you "move up" because in order for you to "move up" and gain higher responsibilities, you have to demonstrate the skills required for the higher position.
Try taking on some side projects, pick up best practices for Agile, learn new programming languages, launch new products. For a technical / product manager, your best bet of moving up is to keep launching products. I aim to launch about 8~10 products a year, about 5 of them are side projects.
That said, in some specific circumstances, when you're the right-hand of the C-levels, it may pay off. But you have to marry the technical expertise with executive skills to move up, so they can see you as "one of them" and justify above market salary and/or promotions.
Suggest tech focused projects that might serve the companies unmet needs. Sales & Marketing might need a dashboard to asses the customer pipeline. The CFO might need a tool to monitor energy usage & costs. Volunteer to help, you'll get known as the brains who figures stuff out.