So I haven't caught up on 20 pages of discussion so these are just my instinctive reactions.
[ ] [BEHAVIOUR] Directed
You will be able to give the Rider moment-to-moment instructions to do just about anything, but you will need to focus most of your attention on it while it is summoned.
Less good for Mathilde in particular, but honestly 'manifest remote controlled cavarly unit' could be very powerful for the Grey order. A single rider sub-battle magic level would allow for great improvements in scouting. Not as discreet as say an Amber's use of birds, but the ability to park yourself in an inn while you send a remote controlled knight to scout out a potential ritual site or beast herd camp is very, very good.
For squishier grey mages, even the "have to give it most of your attention" wouldn't be a bad trade off for the ability to sudddenly have a bunch of heavy cavalry to direct if a threat appeared.
[ ] [BEHAVIOUR] Instinctive
The Rider will lay dormant until someone or something within several kilometers uses destructive magic, at which point it will manifest and hone in on that being and attempt to destroy them.
This is actually pretty amazing, and while it isn't what Mathilde wanted the spell for would absolutely be worth developing with a single rider.
This is "detect a spell being cast within X kilometers and track the caster" spell. That is incredible. Mathilde, with some of the best windsight among modern mages almost certainly couldn't do that unless it was a very big spell and the entire thing was on open plains.
Given the description in the update about how Mathilde wrapped the rider up in hatred of Orc Shamans, Skaven Sorcerers and necromancers, it even seems plausible that it can avoid proccing on friendly casting types.* This would make it an amazing spell for tracking down Orc or Beastman warbands, or tracking Necromancers hiding among the population.
*The obvious downside being if you're looking for say, a rogue College magister who wasn't using Dhar, it would no longer help.
[ ] [BEHAVIOUR] Duel
The Rider will appear at your location and move towards a chosen individual, and will engage them until it or the Rider is slain.
[ ] [BEHAVIOUR] Charge
The Rider will appear at your location and charge towards a specific group of people, and will engage them until it is slain or the group is destroyed or shattered.
Single or Multi target. Personally leaning towards 'Duel' and learning Penumbral Pendulum or Pit of Shades as they're existing and good for the big multi-target needs.
[ ] [BEHAVIOUR] Bodyguard
The Rider will lay dormant until you attack or are attacked by someone, at which point it will manifest and fight alongside you until combat is over or it is slain.
A great answer to "get the mage first" or other sudden ambushes. Probably not what we want right now though.
[ ] [BEHAVIOUR] Ambush
The Rider will appear near the chosen target and strike them once before disappearing. Further strikes will require the spell to be cast again.
Teleporting assassin. Fun for the image of Mathilde combining with Smoke and Mirrors to become Mathilde and her Amazing teleporting Cavalry unit. The teleporting effect is cool for battlefield use, but with them fading away right afterward it seems like it ends up just being similar to existing spells. What is the advantage over say, manifesting a penumbral pendulum on top of them?
Not for me I think.
[ ] [NUMBER] One
1 Knights, 0 additional actions, possibly sub-Battle Magic.
Good for direct and instinctive. Maybe for Ambush and hope it came out as sub-Battle magic. Bodyguard is the only other one I'd consider here, as thee are a number of places where manifesting one knight on a horse might be ok but manifesting several would just result in being crushed by your own magically appearing bodyguards. Even then, you'd have to think about ever going into a tunnel again. Otherwise I'd say no.
[ ] [NUMBER] Trio
3 Knights, 1 additional action, low- to mid-level Battle Magic.
[ ] [NUMBER] Lance
6 Knights, 2 additional actions, mid- to high-level Battle Magic.
I'd say either of these for Duel or Charge. Probably 6 knights. I definitely don't want to commit to three extra actions but six knights is a pretty good and balanced number.
[ ] [NUMBER] Band
10 Knights, 3 additional actions, high-level Battle to Cataclysm Magic.
Pick this if you're one of the hardcore "I never want Mathilde to use the coin and learn Penumbral Pendulum or Pit of Shades, no matter what" brigade I guess.