The PHB refers to engineers in the Gnome race description, however, I find no other reference to engineers as a background. It seems like it would fall into the Guild Artisan category, but none of the business options seem very 'engineery.' Is there a more specific engineering background/ guild business?
There is not an Engineer Background explicitly, no.
The sample backgrounds in this chapter provide both concrete benefits and roleplaying suggestions
PHB p. 125
You might want to tweak some of the features of a background so it better fits your character or the campaign setting. To customize a background, you can replace one feature with any other one, choose any two skills, and choose a total of two tool proficiencies or languages from the sample backgrounds.
You can either use the equipment package from your background or spend coin on gear as described in chapter (If you spend coin, you can’t also take the equipment package suggested for your class.)
Finally, choose two personality traits, one ideal, one bond, and one flaw. If you can’t find a feature that matches your desired background, work with your DM to create one. PHB p. 125-127
In short, backgrounds are flexible, and players are encouraged to work with their DMs to invent new ones if the ones listed in the book don't meet a player's wishes. After all, you cannot possibly cover every 'backstory' of an adventurer with only 13 (25 if you count SCAG) categories.
So, pick a background that is close to what you're going for, then work with your DM to customize it into exactly what you had in mind with your character.
In the player's handbook, there are two workable options. The first is Guild Artisan, which you've already noted is somewhat unsatisfactory. The second is the Customize a Background section on page 125.
The Sword Coast Adventurer's Guide also provides two potential options, depending on how you define 'engineer'.
For the hands-on engineer, there is Clan Crafter. Unfortunately, it replaces Guild Business with Respect of the Stout Folk, which basically means Dwarves like you and may bend over backwards to help you.
For the bookish engineer, there is Cloistered Scholar. You lose Artisan Tool proficiency in favor of an additional language. You also gain Library Access, which grants you a local knowledge store and likely easier access to other libraries you happen to come across. This tends strongly toward being a Librarian rather than a Researcher, but it's easily fluffed that access to special libraries requires some of your time to help out around them.
No, there is not an engineering background, and this makes sense for the default fantasy-medieval Forgotten Realms setting in 5E.
"Engineering" as a discipline in the real world emerged with the Industrial Revolution. Sure, in constructing aqueducts and roads and pyramids and bridges, ancient and classical civilizations engaged in something we might use that label for, but they didn't think of it in that way. From Wikipedia on the history of structural engineering:
Throughout ancient and medieval history most architectural design and construction was carried out by artisans, such as stone masons and carpenters, rising to the role of master builder. No theory of structures existed and understanding of how structures stood up was extremely limited, and based almost entirely on empirical evidence of 'what had worked before'. Knowledge was retained by guilds and seldom supplanted by advances. Structures were repetitive, and increases in scale were incremental.
The default D&D 5E setting is Forgotten Realms, where we have Is there an official reason the Forgotten Realms is stuck with “medieval” technology? — in other words, there's no particular reason to expect that the situation would be any different from the medieval real world. In fact, the need to systematically study engineering would probably be even less, since you can just build with magic.
Of course, D&D settings tend to be random pastiches of appealing heroic settings and archetypes, regardless of actual timelines. That means even though an Indiana-Jones type character is anachronistic, the game bends towards allowing it — see my question on education for archaeologists, and engineering is a similar high-education non-magical career path, and a Jules Verne-style D&D hero seems... unsurprising.
Since the Eberron campaign setting is more steampunk, I thought perhaps there would be an option in the 5E Eberron conversion, but tinkerer seems to be the closest — or maybe dwarf-aligned clan crafter. But tinkerer is rather gadget and small-device focused, and you might not want the dwarf theming; in that case, I think a custom background is currently your best bet. Or, in line with the quote above, perhaps take a second look at Guild Artisan.