I am not sold on the concept for a laptop, mainly as far more is likely to be gained tweaking the OS and settings there or buying a secondary/larger battery (possibly including an external generic charger if the fancy USB stuff of the modern world is a thing for this one), and most laptops that you would consider for such a task already aggressively manage power (even the utter junk will usually have such things) but do it if you want.
It will depend how you are undervolting -- if you are just undervolting for day to day use and leaving the high end it is harder than just 100% all threads until the temperature either equalises or it falls over as that will just stick it into high end modes and that is that. Most conventional tests care more about heat and power delivery than anything like that. You could force it into low voltage mode and see what goes I guess in that case, otherwise you are either concocting an aggressive but still normal test, doing some kind of instant load or having some fun figuring out instructions that might not otherwise make it in time, whether your RAM remains stable or whether the GPU does what it needs to if it is chilling in low voltage mode and gets some instructions to handle and does not have time to ramp up
If you are undervolting across the board and not leaving the high end then standard stress tests will do.
How many times and how long? Always the fun one for this sort of thing, and in this case I expect a battery will age faster than a power supply so you do have a more reasonable case to repeat in a few months. You can run it for long enough that any crash becomes "was it a cosmic ray?" but for the most part most problems should show themselves fairly quickly (possibly instantly, more likely within 5 minutes, half hour is good and if it makes it one or two hours then longer is not going to reveal much more.
As far as "more table gaming" goes then I would only expect that if the laptop normally gets too hot and causes things to crash, in which case I would probably spend more effort figuring out if there was something I could do there as far as making heat removal better.
