I've heard people talk about being so specific with the timing of their rest. I'm not sold that this is a good way to make sure that all things are equal. Here is why...

Some days will simply be better than others. Either due to stress or how much sleep you got or what you ate. Not all days in the gym are created equal to begin with. I would be far more tempted to simply pay attention to how you FEEL your recovery between sets is going. Some days I push things along, and some days I know that it is more important to hit the reps I'm going for than to rush things.

Now, assuming you are not working with % intensity as your primary factor for determining advancement (you don't base your gains on a rise in your 1RM) then I'll assume the goal is to get more reps than last time? Perhaps a little bit of both somehow? Regardless, the only time I would worry about manipulating time is if TIME is how you are judging progress. For instance, Last weekend I did 40 flips of my 500lb tire. I gave myself 30 seconds to complete each rep, and I had decided that I would stop if I could not complete each rep in that time period. Turns out this was actually pretty easy. I was sore none the less, but completing the full set wasn't an issue. I can't go up and down in weight... the tire is what it is. Because this is almost purely metabolic conditioning for me, reducing recovery time is important. I would like to be able to reduce my flips down to something in the 5-6 second range and still knock out 40 reps. That is a long way from here, but it is a goal. Next time I do this work (about once a month, perhaps) I will drop my rest times. Maybe something like 25 seconds. In this case monitoring time is important, but in all of my other work... not so much. Why? Because I have decided that the important thing is to nail all my reps at a certain intensity. No more, no less, just get what I need to get and be done with it. If the goal was to just get one more rep (and some of my lifts use this protocol, though it is typically a bodyweight exercise) then I set a total time, and the goal is to cram more work into the same time frame. Rest isn't important. If the work is being done faster, then more rest might be needed. I'm not worried about rest times, only how many situps I can knock out in 2 minutes, or how many pullups... etc.

So you may want to figure out what the measure of your success is. If it depends on you completing reps, then watching a clock isn't as important as being rested.