First of all this is not a good rule. The rules for reflexive pronouns are very complex, which is probably the most important thing to know. Nonetheless, here are some generalisations we can make:
We require reflexive pronouns when they co-refer with a noun phrase earlier in the immediate clause, or within a larger noun phrase:
- John described himself. (coreferent within clause)
- John's letter to himself ... (coreferent within noun phrase)
There are some basic caveats to these two descriptions. One of these, for example, is that when the pronoun occurs within a locative phrase, we do not need to use a reflexive:
- He placed the book beside him.
No reflexive is required in the example above because him is in the locative phrase beside him.
Notice that the coreferent does not need to be the Subject of the clause:
- I gave Bernie a picture of herself.
In the example above, Bernie is not the Subject of the clause, but the Indirect Object.
Importantly for the question here, even when the verb in question has no expressed Subject, the reflexive pronoun is used when it is understood to have the same identity as the notional or understood Subject:
In the imperative above, the understood Subject of the sentence is, or course, you. Because the word yourself corefers with this notional Subject, it must be reflexive.
This point explains the difference between the Original Poster's first two examples:
- It's difficult enough organising myself, let alone organising someone else as well.
- It's difficult enough organising me, let alone organising someone else as well.
In these sentences the pronouns occur within subordinate clauses headed by the verb organising. In the first sentence the notional Subject of this verb must be analysed as me. The reflexive pronoun myself is co-referring with this Subject. In the second sentence the Subject of the verb organising needs to be determined from the context. We could conjecture that perhaps the notional Subject is the speaker's carer. The two sentences would then mean:
- It's difficult enough [me organising myself] yet alone me organising anyone else.
- It's difficult enough [my carer organising me] yet alone her organising anyone else.
In the second sentence me does not co-refer with an overt or notional Subject and therefore me is not reflexive.
We now move on to the case of override reflexives. These occur in a very limited amount of situations when the pronoun is a Complement of the verb, but does not co-refer with another noun phrase in the clause. These have been being used for eons although prescriptivist hacks might lead you to believe otherwise. Here is the introduction to reflexive overrides in the Cambridge Grammar of the English Language, 2002:
CaGEL then goes on to explain the very specific situations in which an override is possible. One of these is when the pronoun is the Complement of the verb BE when used in its specifying sense. Here is the description of overrides with regards to Predicative Complements and the verb BE:
This is the situation that we find in the Original Poster's fourth example:
If it's just myself at home, I leave the dishes until the next day.
Here the pronoun myself is the Complement of the verb BE used in its specifying sense. Therefore a reflexive pronoun is admissible. Of course, this is an override, so the more frequent usage would be with a regular pronoun, as in the Original Poster's third example:
If it's just me at home, I leave the dishes until the next day.
Both of the above are completely grammatical.
The CaGEL go into some depth about when overrides are and are not possible. It is not straightforwardly the case that we can override in every case of the pronoun being the Complement of specifying BE, for example. If you would like to read more about override reflexives, you can do so here: CaGEL 1494. If you would like to read more about reflexives in general you can do so here: CaGEL, p. 1483. If you would like to read about the emphatic use of reflexive pronouns, you can do so here: CaGEL, p. 1496.