I don’t think this is the solution - but it’s close. The indicatrices are meant to be ellipses, no matter what the projection. I have a suspicion that if one worked out the shape of a very small circle (say 10 m radius) in the map projection, and then magnified it, this would be closer.
Here’s what the 14 degree radius circles look like in the Cylindrical Equidistant projection:
The shapes on the 60 degree north and south meridians aren’t ellipses. I started putting together a very hacky script using mapproject and awk to try and get ellipses. It’s not working yet.
In the meantime, maybe your solution could be called Wessel’s indicatrix 
Edit: subsequent Google searches show examples of Tissot’s indicatrices which look like the squashed ellipses in the cylindrical equidistant plot above. But the mathematical description says they should be true ellipses. This thing is irking me enough that I’m going to work out a solution and post it here