The program does not specify rest periods. The only guideline is to rest long enough to get all your reps.
IMO, more rest is better, if practical for you, because it allows for better recovery from set to set and day to day, making it less likely to hit a plateau. But it also depends on what version of the program you are doing -- the number of target reps, whether you are doing weighted pullups with a goal of increasing weight or BW pullups with a goal of increasing max reps, and how close to your max the target number of reps actually is.
For instance, I've done a lot of cycles of the 3RM program with weighted pullups. This starts with a top set of 3 and builds to a top set of 5. I have found that it was much more sustainable and I made more overall progress if I used a weight that was NOT an actual 3RM. In fact, it worked much better to use a weight that I could already use for a challenging set of 5 (not even a true struggling 5RM). A cycle through the program would result in that challenging set of 5 becoming a comfortable set of 5. Then I would reset the weight to make a set of 5 challenging and run another cycle. This was sustainable for many cycles.