there are no “politics” for someone to get accepted or denied into Hatzolah.
If your neighborhood is looking for new members, and they feel you are sincere in your reasons for wanting to join Hatzolah, with gentle persistance you eventually will get accepted-
In many cases the people with “connections” are the ones that do not get accepted right away- it is a case of “who you dont know” as opposed to “who you know”.