Would you have been happier if I had used the words "radar contact
isn't required to issue the initial heading issued to an aircraft to
provide navigational guidance by radar."?

No, because you changed the wording. If it actually said that, you'd
have a better argument, but it says "heading issued FOR THE PURPOSE OF
providing navigational guidance".

This convoluted wording can easily be interpreted to mean that the
heading is to put an aircraft in a position to receive radar vectors,
which requires radar contact. This, in fact, is what I think it
means.

A purpose for the heading is not necessary, since pilots operating
in a radar environment associate assigned headings with vectors to
their planned route of flight.

Yes, it says pilots ASSOCIATE headings with the vectors which will
come once the aircraft has been radar identified and subsequently
issued a heading. It doesn't say that a heading IS a vector. Big
difference.

Please give an example of a heading issued by ATC in a radar
environment that *is not* "issued for the purpose of providing
navigational guidance by radar" and therefore *is not* a vector.

If a controller has established radar contact with an aircraft and
then offers a heading, that is a vector.

Until radar contact has been established and a heading issued, the
aircraft is effectively "non-radar". (I don't care much about
aircraft separation....that's your problem.)

"Avoid the use?" You mean like when they say "...is to be
vectored

Yes, IS TO BE. This is future tense, as in indicated that the
aircraft is not currently being vectored but will be once certain
conditions are met.

TURN LEFT/RIGHT HEADING (degrees)" and not "TURN LEFT/RIGHT VECTOR
(degrees)

A vector requires radar contact and a heading assignment, so the use
of the word "heading" in a vector is entirely appropriate, because
he's already been informed of "radar contact."

However, the use of the word heading in 5-8-2 is outside radar contact
and doesn't fall into the defintion of vector.