Ultimately, the restrictions on activities during rage are open-ended: patience is not a defined thing under the rules. That part of the rage rules is left there for a DM to rule as they see fit, as an ad hoc, “I know it when I see it,” kind of thing. This is a reflection of the fact that characters can get up to any conceivable activity, and the rules cannot possibly cover them all: they’re literally infinite.
That said, the things that the rules do cover are fairly clear, and also meant to be illustrative, I think, for DMs needing to adjudicate uncovered situations. That is, I think it is implausible to suggest any intent or expectation on the authors’ part that DMs would substantially expand the kind of thing blocked by rage, rather than simply extrapolate from what we have to handle situations that the rules don’t cover.
To wit: if we have rules for an activity, then we should also have clear rules for whether or not rage blocks it, mostly whether or not that thing requires concentration, which is a defined term in the game. That is, the rules clearly indicate when things require concentration, because such things interact with the Concentration skill (and also with other mechanics, such as rage itself). If you have defined rules for things and those don’t note that the thing requires concentration, then you can do that thing during rage. This covers supernatural abilities like a paladin’s smite evil, for example—those definitely do not require concentration, and so definitely can be used with rage.
Well, I say “definitely,” but as I said originally, the rules really are open-ended: “patience” is pretty much up to the DM. Anything could be said to require some patience. But at that point, you could even include clearly-meant-for-raging-barbarians activities like attacking, which requires an element of timing. Rage doesn’t even prevent the use of Weapon Finesse or sneak attack. Supernatural abilities are magical in some fashion, but they are “natural” to those who have them, possibly even more so than making a trained weapon attack. So while the rule is open-ended, I feel pretty confident that I can say that smite evil is “definitely” allowed. Ruling that it is blocked would be inconsistent with the precedent that we have.
So that covers everything that has rules: if it says it uses concentration, you can’t do it during a rage. If it doesn’t say that, you’re fine. There may be some corner cases for long-term, “downtime” activities where the failure to mention concentration may arguably be an accidental omission on the authors’ parts, since they likely never imagined that such activities would ever need to interact with stressful situations such as those covered by the Concentration skill. For example, item-creation never says it requires “concentration” per se, but it definitely requires focus and a lot of time, and rage definitely blocks that. Extending that precedent for such cases would be reasonable. You’re also fairly unlikely to want to use rage during such times anyway.
For times when you might actually want to use rage—combat, mostly—you’re not talking about any long-term downtime activities by definition. And for those things which have rules, we can expect those rules to specify if concentration is a factor—and we can expect that, if they don’t mention concentration (and aren’t Charisma-, Dexterity-, or Intelligence-based skills that aren’t Balance, Escape Artist, Intimidate, or Ride), they can work with rage. For factotum, that means everything except ardent dilettante—which is spell-like and therefore explicitly requires concentration—can be used in a rage.
