Question: what, specifically, does a "pulse" amount to? How long is it, and how long of a pause do you need to have between pulses? Where do you find reliable information on that, and do you keep track of the different definitions for all your different batteries?
Unfortunately, the answers to those great questions are complicated. I'm a vaping noob but have been spec'ing cells and designing power supplies, battery chargers, battery management/protection systems, battery dischargers, and other related devices since 1992. Here's my take....
A "pulse" can be anywhere from microseconds to seconds long. It all depends on the industry and application where the cells are being used and what the parties involved define a pulse as. Vaping definitely is on the long end of the range of what is considered a pulse and may be considerably longer than what the cell manufacturer or reseller considers to be a pulse.
To make things worse, a pulse rating is not a firm specification on its own. It is tied to duty cycle, cell life, ambient temperature, and other factors.
As you mentioned, the rest time between pulses is important. It allows the heat that has built up inside the cell to migrate outwards. This evens out the internal temperature of the cell, eliminating damaging hotspots, and lets the cell cool. The duty cycle, or ratio of the pulse on time to the off time, is extremely important and has to be part of any pulse current rating. For example, one 4 second pulse every minute might not be a problem at all. But, one 4 second pulse every 5 seconds might easily cause the cell to overheat and vent (or worse).
Cell life can also be affected by the pulse rating. A cell might have a pulse rating of 30A but how much does that effect cell life? Cell manufacturers are typically very conservative in their ratings but resellers often aren't. A cell could easily be spec'ed anywhere from 10A to 30A pulse, depending on how long the person who is rating the cell wants it to last. An application that draws 10A pulses might result in a cell that last 500 cycles. An application that draws 30A pulses could shorten that to 150 cycles.
Bottom line...you need to know the other related data to judge whether a cell has the spec rating you need. You'll never get that from the manufacturer or, most likely, the reseller. Due to all the variables, the manufacturer will always say that you need to test their cells in the application you're considering. They can only give you their nominal specs, listed in the data sheet. And the reseller typically just doen't have the time to test all their cells for all the different uses those cells might see. Third party testing is typically how you find the info we need to judge whether a cell will perform the way we want for a particular vaping setup. Other enthusiasts often post their cell test results and sometimes the results can be directly applied to your application. Sometimes you have to piece together results from several different tests to extrapolate how the cells might behave for you. <deep sigh> It's often very tough to do!
To simplify keeping track of all this info, I'll settle on just one cell make/model for each broad application I need them for. I note their max ratings (from my own testing) and just use the best cell for any new application that pops up. Doing your own testing is a great option if you have the time. The West Mountain Radio CBA IV Pro battery analyzer is a fantastic device to test cells with. It has highr ratings but I recommend 100W/30A maximum for long device life. I have several constant-current electronic loads (battery dischargers) here that I have designed but so often turn to the CBA for a quick test because of its convenience and ability to store and later review the discharge graphs it produces (voltage vs time, Amp-hours, etc.).
[edit] another important pulse-related rating is how much does the cell temperature rise for the pulse? The rating is almost useless without this information. If the cell rises to 80C case temperature for a certain pulse, cell life will really suffer. However, if max case temp is 40C after the pulse, then no problem. Remember though that cells used for vaping are sealed in a box/tube and cool very slowly. We cannot just keep pulsing them at their max rating without taking into account heat buildup. You need to derate the cell's pulse rating based on the duty cycle, i.e., how often you draw. By how much? Unfortunately you need to test, test, test.