Look at CRT draw in slow motion. You have an ultra bright flash, then an alarmingly quick phosphor glow falloff.
You'd need, basically, a high hz HDR monitor with an actual sub-ms response time... so you can superbright blink the character, essentially black framing it.
The rest of the actual softness of the glow can be emulated conventionally with shaders (there are some super swanky terminals and emulators that have that part already done).
Although this flicker would indeed be necessary for a 100% accurate reproduction, I'm not sure that is really the thing that current CRT shaders are missing for feeling "just right". After all, the linked example image feels very convincing and yet is static.
Could that be due to something like the phosphor glow having non-linear properties or something?