How much time do pilots have to execute a TCAS Resolution Advisory?
It depends a bit on speed but your linked article has the answer 



Traffic advisories are provided 35-48 seconds out and a Resolution will be provided 20-30 seconds out. Since the resolution is coordinated you only need enough time to clear the other aircraft however the greater separation the safer it will be so its advised to respond immediately upon a resolution being provided. Immediately means as fast as possible.  

The FAA's TCAS II outline document states that modeling was performed assuming the pilots responded within 2.5~5 seconds 


  In modeling aircraft response to RAs, the expectation is the pilot
  will begin the initial 0.25 g acceleration maneuver within five
  seconds to an achieved rate of 1500 fpm. Pilot response with 0.35 g
  acceleration to an achieved rate of 2500 fpm is expected within 2.5
  seconds for subsequent RAs.