When the trail is sketchy or when following animal trails I find it counterproductive to focus on staying on the trail or finding the trail. Know where you want to end up in a couple hours and calculate where that is approximately in relation to where you are now. Constant evaluation of this develops some uncanny skills in this area.
Also look a ways ahead for places where the trail probably exists. Examples: passes, cols, easy stream crossings, channels around cliffs or intense brush. Chances are someone else or an animal used this and the trail probably crosses here.
Pay attention to lineations and wavey lines in the landscape. These can reflect rock structure, strata, faults, erosional and depositional patterns, and vegetation patterns on a grand or small scale. These are often the best routes and a trail might just be there. You might even find them a better route than the sketchy trail.
Know your local vegetation. An old growth forest is much easier going than brush in in many parts of the world. Alpine tundra plants like Alpine bear berry can be traversed much easier than wet tundra plants such as grasses and sedges, etc. You can spot patterns of these plants at quite a distance when you know what to look for.
You need to use trails to advantage, not be tied to them in backcountry.