Frankly, few mature companies need a "engineer/product guy" and your split experience will work against you unless you make it clear that you're earnestly committed to one of those roles in particular (are you?), or you specifically look for work close to sales at B2B or contract development firms, where the combination of those skills is an asset when selling and sometimes prototyping custom work.
You're selling a product right now (yourself) and you need a clear understanding of what the product is. It's not a typical engineer and it's not a typical product person. It's not even an practiced corporate drone. So don't expect to sell it as one of those things and don't distract yourself applying for work that needs them (your resume will be ignored in this market). Instead, figure out what niche value your background brings and focus directly on selling that to the customers (employers) that would need it.
You're selling a product right now (yourself) and you need a clear understanding of what the product is. It's not a typical engineer and it's not a typical product person. It's not even an practiced corporate drone. So don't expect to sell it as one of those things and don't distract yourself applying for work that needs them (your resume will be ignored in this market). Instead, figure out what niche value your background brings and focus directly on selling that to the customers (employers) that would need it.