Marketing has 4 general components- Pricing, Placement(channel) Promotion, and Product. For these 4 P's the PRODUCT component is probably the best fit for combining marketing with engineering. As a product manager, you wont normally do the engineering, but will need to understand what your development engineers communicate to you. You will need to be able to think about not only what the product will do, but how the design of the product or service will be presented or used by your customers. The design of the product itself, along with the end to end design of the customer experience are all critical components that could use your engineering talents.
Consider your use of some new product or service. (Maybe purchase of broadband internet or cable tv) How easy was it to get the information you needed to make a buying decsision? Once you decided to purchase, how easy was it to make the purchase? Was tracking and follow-up information provided readily or did you have to go in search of it. Was therer a guaranteed delivery date? How was the product or service delivered and how much involvement from you was required? Would you have desigened the product or the delivery process differently? Think about what you and other consumers in different groups might expect as a buying experience.
Another very good carreer choice would be a "Sales engineer" or similar (SA, SE, etc) These are more technical sales people who take the products offered by a company and work with the sales or account manager to help the customer choose the right products and build the solution that would best fit their goals. Less engineering and more technical sales, but still doing both marketing and engineering of sorts.
I suppose that as an engineer- You might be able to work to advance marketing tools and techniques using technology or engineering. Maybe develop new ways to promote products, such identification of a user through Near field, wifi or some other technology so that as the consumer walks buy- it looks at their browsing history to provide customized content for them ( i know this already exists- but it isnt widely used with billboards or other signage today- though malls are adopting quickly). You might also develop some other methods of product placement or sales channels as an engineer.
I think it is important for you to think about what you like to do. Do you want the responsibility for running an entire product and being responsible for it's success or failure, not just because of how it was designed, but also how well you used the other 3 P's to get the product out in the market and sold. This is what a product manager does. If you ike dealing with customers and helping them solve their problems, then maybe the SA/SE role might be a better fit. Less overall responsibility for the entire product and more responsibility for positioning solutions and reporting back to the Product team when issues arise.
If you really want to remain more of an engineer that designs things, then maybe working as part of a product engineering team in the engineering department might be a better fit.
My very best advice is to figure out what activities you like to do. Find out what drives you and makes you happy and fulfilled in a job, then pick the job that best fits that.