#1 The Government is minded to support the amendment.
#2 The Government are minded to support the amendment.

I can confirm that the latter is an equally acceptable alternative for
me in British English, although #1 might be considered more formally
correct. But I think we'd always use #1 if we were talking about the
government as an institution, rather than as a particular group of people.

#3 The government is our servant.

The police, on the other hand, feels decidedly plural. I wouldn't use
#5, although a quick trawl of Google News suggests that it might be
acceptable in some parts of the English-speaking world (including
India and the Caribbean), at least as an alternative. But either
singular or plural sounds okay to me when a particular police
authority is the subject.

#4 The police have denied these claims.
#5 ??The police has denied these claims.
#6 South Yorkshire Police { has, have } denied these claims.
#7 The police is an institution which enforces the law.

As in the case of the government, in #7, I'd use the singular verb,
because there the police is a more abstract idea, an institution,
rather than a group of people doing something on a specific occasion.

*

Back to Old Norse, there's a curious example in Skáldskaparmál where
neuter singular used in place of masculine plural. I don't know why
that is. It doesn't seem to be a conflict between natural gender and
grammatical gender.

#10 hér er kallat hvalir Viðblinda geltir
here whales are called Viðblindi's boars
(Skáldskaparmál 46)

I wonder if it's a similar phenomenon to the English fluctuation
between singular and plural in sentences like the following, #8 being
a colloquial alternative.

#8 there's four of them
#9 there are four of them