I decided to delete the accounts (except the main one) and then added them back again.
Looking at the groups, it appears that the additional accounts are members of more groups than the main admin account but they were things like "fax", "tape", "video". So I removed these to get it as close to the main account as I can. Though using the checkboxes in the user admin panel, I can't seem to get the accounts to be identical, for examplke, there isn't a checkbox for "dip" whatever that is.
I did make sure that the checkbox for "connect to wireless and ethernet networks" is checked.
The main account groups are;
The additional account groups are;
When I log on under the additional account, I still don't see any icon to manage the wifi connection.