Now, from my very limited understanding the 4th official is there as a back up referee if one of the them gets injured. As well as, manager, bench and coaching staff control and substitutes. This sounds like a lot but consider, this. They are the ones who deal with the subs so they could stop the clock for that quite easily. Same with injuries, they know when treatment occurs and know when medical staff run on the field meaning play is stopped for longer than usual. So, stopping the game clock is just an extension of those two circumstances. I think a VAR check and goals being scored are both obvious.
Those changes I think would be made with a relatively seamless transition. Free kicks, Goal kicks, Corners and throw ins are the hardest to police. Players take them quickly; they occur very often, and it can sometimes be hard to understand what decision has been given. I think for goal kicks, corners and free kicks/penalties the clock could stop on the referee’s whistle. As soon as the referee blows the whistle the ball is dead, game clock stops. It restarts on the referee’s whistle or when the players take the kick, some refs allow quick frees to take place others are insistent that it must be on their whistle.
If not the 4th official, then VAR should be able to handle it. I know they do dozens and dozens of checks throughout the game and I think for that reason if the 4th official isn’t the one keeping the time, then it should be VAR. If you really had to you could appoint a timekeeper, we already keep track of what time events occur during the game, just look at any live commentary report and you can see when players do everything besides throw-ins.
These are of course just my opinions and my thoughts that I have had about football Let me know what you think by commenting or messaging me one way or another