How fast can the brain react in order for someone to pull a trigger? Just out of curiosity, regardingly highly unlikely situations of ever needing to disarm someone - using neuroscience to make informed self defence decisions:

How fast can the brain recieve a visual or reflexive (seeing me beginning to move my hand, or feeling my hand hit the wrist -- I suspect the two impulses might have differing response times) signals from the body, to the moment of signaling the finger muscles?
Short answer
The motor response latency to a visual stimulus is approximately 210 ms.

Background
You are basically asking for the visually induced reaction time of a motor response. Reaction times have been assessed many times in various studies. In a very recent study with an impressive subject population of more than 1400 (aged 18 - 65), the motor response latency to a visual stimulus was estimated at an average of 213 ms. Reaction times increased with age, but were unaffected by sex or educational level. Old age mainly affected the motor latency, and not so much the visual processing speed.

Reference
- Woods et al., Frontiers Human Neurosci (2015); 9:131-12p