"Engineering" here means "modeling."
You need to build a mathematical model of the process, using variables for the unknown quantities. Then determine the values of those variables empirically i.e. via experiment.
While that statement may be intimidating, if you can solve the "how long does it take the train moving at a speed of 45mph to travel 105mi?" class of problems, then modeling this bottle line will be straightforward.
What I can say is that, if you are going to start the timer as the fail bit gets to a particular position, and that position is the one to use when the speed is 100% i.e. when the timer delay will be 0 i.e. no delay, and trigger the reject device at timer expiry, then the increase in delay from 0 will not be linear with decreasing speed. I am not saying that a linear characteristic won't be "good enough" from 100% speed down to 50% speed, just that the actual relationship between line speed and delay would not be a line of you plotted it.
However, if you model the process, you will see that
@Steve Bailey's suggestion earlier, to adjust the bit
position to examine for a fail bit, where the magnitude of the adjustment is dependent on line speed, is a much simpler approach, both to model and implement, and that position adjustment magnitude
is linear with line speed.