Send e-mail to admin by new user registration

[merefield (Robert)]

I’d gladly look at this for you, but doesn’t this solve your problem?:

Email notification for "must approve users"

The frequency of the reminder is controlled by the pending users reminder delay site setting. The default value of that setting is 8 hours. Try setting it to a lower value. The pending user notifications are triggered by a background job that is run once per hour. This means that setting the pending users reminder delay to 0 will still cause the notifications to only be generated once per hour. Note that these notifications are only sent to site moderators, not to site admins.