verbs - When must a gerund be preceded by a possessive pronoun as opposed to an accusative one?

I was recently reading this very interesting post here:

When is a gerund supposed to be preceded by a possessive adjective/determiner?

In this thread, it is argued persuasively that we could use either his or him interchangeably in front of a gerund. However, this does not seem to me to be true. For instance, consider the following example:

• His continuous meddling was starting to bother me.

It appears that only a possessive will do here and an accusative is completely ungrammatical (in the true meaning of the word):

• *Him continuous meddling was starting to bother me.

An accusative also seems to give rather dubious results in the following examples too. Compare:

• The senate characterized their sinking of the flagship as rash and excessive.

... with the completely ungrammatical:

• *The senate characterized them sinking of the flagship as rash and excessive.

So, it seems that we cannot just freely exchange the accusative and possessive pronouns that occur before gerunds.

My questions therefore are:

1. When must a gerund be preceded by a possessive pronoun as opposed to an accusative one?




2. Are these gerunds, and if not why not?