There is nothing called "Gulf Arab country" to begin with. It's Eastern Arabia which is an ancient historical region.
Eastern Arabia - Wikipedia, the free encyclopedia
Other than that an Arabic dialect that is spoken in mostly the coastal regions of Eastern Arabia. In KSA less than 200.000 people speak a Gulf Arabic (Khaliji) dialect. Aside from that a musical genre.
Khaleeji - Wikipedia, the free encyclopedia
Culture of Eastern Arabia - Wikipedia, the free encyclopedia
Gulf Arabic - Wikipedia, the free encyclopedia
Khaliji (music) - Wikipedia, the free encyclopedia
Nor do you have to border the Gulf to become a potential member. Yemen for instance is an Arabian country as they get and located on the Arabian Peninsula but not a member. Yemen "only" borders the Red Sea and Arabian Sea.
Basically it's a union of neighboring monarchies on the Arabian Peninsula with shared interests although the countries are distinct just like every historical region in major Arab countries are.
This union might expand one day among Arab countries as the likes of Jordan, Morocco etc. (also monarchies) have expressed interest in joining.
Iraq too.
Yemen too.
Iraq
Iraq is the only Arab country bordering the Persian Gulf that is not a member of the council. The associate membership of Iraq was discontinued in 1990 after its
invasion of Kuwait in the
Gulf War.
[57][58] In 2009, it was reported that Iraq was set to join the cartel of the GCC Chambers of Commerce.
[59]
In 2012, Iraqi Defence Minister
Saadoun al-Dulaimi stated that Iraq wants to join the GCC.
[60] Kuwait supports Iraq joining the GCC.
[61]
Gulf Cooperation Council - Wikipedia, the free encyclopedia
Defense Minister confirmed that Iraq seeks to join (GCC) Gulf Cooperation Council - Iraqi Dinar News, Information and Facts - IRAQI DINAR
In the current political climate Iraq cannot join GCC. In a perfect world they should join as a neighboring brotherly Arab country if they want to do that. It's better to cooperate than to be enemies. Especially as brotherly people. A lot of benefits mainly economical.
Anyway there is no hope for the MENA region with this current generation in power so it's irrelevant really. The silly enmities will continue and brother will continue to kill brother and more mothers will cry.