I would not take any advice, here, about that. The answer really depends on a number of factors. The problem with cutting a hole in your mast is that the strenght of the mast largely depends on the integrity of mast walls. (This is called "monocoque" or "semi-monocoque" in aviation construction. Might be the same term when referring to masts.) Think of an aluminum beverage can. It is pretty strong so long as you don't compromise the walls. But, as soon as you put a small dent or hole in the side, the structure is significantly weakened.
I do not know enough about mast construction to know to what degree this is true across all masts. My assumption is that lighter-weight masts will have less tolerance for this and will be more dependent on monocoque strength. Fortunately, the bottom several feet of the mast do not rely much on resistance to lateral stress. It is mostly resistance to compression that matters, at that part of the mast (and arguably, most of the mast).
If I were to attempt this, without consulting a good rigger, I know what I would consider. It has less to do with the distance from existing holes and more to do with the absolute position of the new hole and also to do with the absolute amount of material removed.
In general, I don't like to tell people, "Don't do it. Hire a professional." But, this might be one of those times. At minimum, by consulting a rigger, you will get an answer as to whether this is advisable at all and, if so, what the considerations are. Just be upfront about your intentions (obviously) so they don't spend time/effort giving you free advice with no chance that you will hire them for the actual work, unless they know that's what they are doing.