I've flown thousands of hours using 1:60. Not just across desert, farmland, bush, towns or wherever but also for tasks such as finding the height of a weather radar return, finding a lead bearing for starting a turn to intercept a radial/localiser beam, determining maximum drift for a known or estimated crosswind component etc.
Pretty much anytime you need to convert an angle to or from a cartesian coordinate that involves our hexigesimal time or angle systems.
Off track corrections can be done in your head to an acceptable level of accuracy. You only need remember '1, 2, 3, 4 & 1 and a half' and when to use those numbers. It's a three step problem: First to stop diverging from track any more, second to fly towards track, and third to maintain track again.
Step 1: Find the angle of the divergence from track (Track Error or TE) to use to adjust heading to stop any more drift.
Step 2: Find the angle needed adjust heading to close towards track, regaining track at some chosen point (Closing Angle)
Adjust heading by both those amounts ie Track Error and Closing Angle, and then:
Step 3: Remove the closing angle so you maintain the track you just regained.
Step 1: Track Error
If you find yourself off track and have flown any distance that is something like 60nm (say 55nm to 75nm or so) then multiply the distance off track by '1'. For example, flown 55 miles since last on track and fix your position 3 miles off track then multiply the distance off by '1' to find the angle by which you diverged away from the desired track. In this case 3 degrees. If you alter heading by 3 degrees towards track you will parallel track.
If you have flown somewhere around 30 nm use '2' eg flown 34 nm and find yourself 4 nm off track: 2 x 4 equates to 8 deg drift. Alter heading 8 deg towards track to parallel track.
Flown around 20 nm? Use '3 times' eg Flown 19 nm and are 2 nm off track? 3 x 2 equates to 6 deg Track Error. Alter heading 6 deg towards track to parallel.
Flown around 15 nm? Use '4 times'. 16 nm flown since last on track and 1 nm off track? 1 x 4 = 4 deg off track.
If the distance flown is about 45 nm then use 1 1/2 ie 1 x the distance off track + another half of that eg flown 42 nm and 4 nm off track: 1 x 4 = 4 degrees + an extra 'half' of that figure. 2 in this case so Track Error = 6 deg.
Step 2: Closing Angle
Choose a point where you would like to be back on track again. It could be the destination, next turning point or even just some feature that is easy to find.
Use the same method as for Step 1, but use the distance from your present position to the chosen point on track. For example, the point where you would like to regain track is 35nm away and you're 4nm off track. 2 x 4 gives 8 deg needed to alter heading to close track.
Adjust heading towards track by the amounts you just worked out in Steps 1 & 2.
Step 3: Maintain Track
Later, when back on track, adjust heading to remove the Closing Angle found in Step 2 eg Track Error was 6 deg, Closing Angle 8 deg gave total heading adjustment to get back on track of 14 deg. Now that you're back on track turn towards your original heading my 8 deg. That leaves you with your original heading corrected by the Track Error only.
Using the method requires only a few measurements : Distance Run since last on track, Distance to go to get to the back on track position, and distance off track, and only takes moments to do. It's usually possible to see ahead of time where you will fix your position off track so those measurements and even the calcuation can be done ahead of time so when you fly over the off-track fix all you need do is turn towards track by the calculated amount and log the time.
Further, the Distance Run & Distance to Go you measure can then be used to find your groundspeed and revised estimate for the destination/on track fix, killing two tasks with one set of distance measurements.