The Animas Forks / Silverton side of Engineer right below the pass is pretty steep. I wouldn't want to do if muddy. However, this loop is a main tourist attraction and is maintained more than you might realize.
The section of Engineer from Animas Forks towards Ouray (sometimes called Mineral Creek) is less maintained and more technical. An un-lifted truck is more likely to scrub on a few rocks here.
No trip to the area is complete without a run over Imogene Pass plus I'd highly recommend doing California Pass/Hurricane Pass/Corkscrew Gulch.
Here's a great resource. Be sure to look at the nearby tabs to see all the adjacent trails. Download their gpx files into something like Gaia if you're not doing that already.
Engineer Pass is well known as part of the iconic Alpine Loop trail network in the high San Juan Mountains. Many roads criss-crossing over the peaks were established during the late 1800s to support mining operations seeking gold, silver, lead, and other ore deposits. These trails provided...
www.trailsoffroad.com
One mistake many make in visiting this area is not realizing the window for these trails being clear is so narrow. July, August and maybe September are your best bets. If you come early in the season (June), keep an eye on this status page to ensure your destination is clear:
Colorado High Country Status - Trails Offroad
If you are interested in any company, share your plans and invite others. You might find someone to travel with...including myself.