Can we trigger kill-cams manually via Papyrus or spell?

No.

Yes it's possible via scripts
"Simple melee tweaks" allows to trigger a killcam by activating a bleeding out enemies and "sneak tools" by activating a sleeping enemy or that hasn't detected you.

You should check these mods

This is not a kill-cam though, you can play the animations but cannot manipulate the camera by using scripts to trigger the exact kill-cam we usually see ingame.

Depending what you are trying to do maybe. They are determined by conditions on the animations so you could modify the kill cam conditions to be the existing conditions OR a has magic effect/has perk/conditional script property you toggle on and off as you want. The player'd still need to attack and you'd have to account for script latency but it should work. With skse you could probably also get the key bound to attack and then force tap it to activate a killcam in a cutscene or something.

Yeah, I started to look at camera nifs. But I've not spent time to learn its systems. I simply opened one up, browsed its nodes then closed it. I'll need to research how it works.

Basically, I want to implement a "glance back, right and left" while horse riding with a press of the arrow keys. Of course, if I get that implemented, there are other uses for this apart than when mounted.

So, it's not as simple as sending an animation to the player to force a camera change.

Unless I get enough of an idea of the animation system and how to set-up changes to the camera depending on conditions.

Thanks for all the suggestions. They've pointed me in the right direction, I think.