Many thanks to Brian & Euler,

I found the INI file but I wound up going the safer route.

I created 8 identity copies and deleted the 8 originals.
I then created 8 new copies giving them my original identity names.

So I now have my original identities logically ordered [:D]

I have 8 identities in rather a haphazard order.

Can they re-arranged into a more logical order?

Yes.

With Pegasus Mail closed edit the "[Pegasus Mail for Windows - Identities]" section of the PMAIL.INI file to your preferred order.  I strongly suggest making a backup copy of PMAIL.INI first.

The PMAIL.INI file is located in your new mailbox directory.  If you don't know where that is use the Pegasus Mail "Help" pull-down menu and select "About Pegasus Mail..." then click the Info button.

Also, you can use Pegasus Mail Identity facility (e.g. Tools > Identities...) this way:

Let's say you have 4 Identities in the following order: 1, 4, 3, and 2 and you want it to be as 1, 2, 3, and 4. All you need is to ADD a new Identities providing a different names and following the desired order. In the field Name for new identity: put say New1 and them in the field Base new identity on: select 1. The newly created Identity, and identical copy of the old, will be put at list's bottom. Now you can delete de old Identity and repeat this procedure with the next one, and so on. At the end you'll have your Identities as you like.

This method is more laborious than the one described by Brian, but safer IMHO.[;)]