I found a gem!

OpenTopoMap is the best free mapping service for hiking and cycling that I have found, but it gives no indication of whether a path is a right-of-way. In contrast UK Ordnance Survey maps do show right-of-ways e.g. here and I include an excerpt below for comparison, moreover this site is devoted to showing them. 

My track 12.6 miles

The gem, in OpenTopoMap

Same area in Ordnance Survey 1:25000

So, I headed north along the Tiverton Parkway cycle route and found the entrance to the "gem" between the station car park and the small pond.  This path is omitted on the Ordnance Survey and FPM maps because it is a "permissive path" and not a right-of-way, and yet the land owners have done an amazing job: lush cut grass underfoot, occasional areas with picnic tables, and appropriate well maintained fencing and gates.

Check out my photos below. Click on any of the images to zoom in. 

Note the GWR up and down trains passing...

...in the near distance

No, I didn't ingest any without relizing (sic) it!

This right-of-way crossed someone's garden

I followed this typical Devon road

View from highest point

 And on the way back I checked out that elusive footpath at Whitnage.