So I am shifting my focus from puppets to puppet...sorta.  The focus will be on my mascot, Tyger, as he explores his and others dreams.  One of his dreams is to be a puppeteer.  So he will create several Glorified Sock Puppets to use.  My first though was to build two of each puppet, 1 full size and another 50% and set on a mechanism that controlled mouth movements.  Trying to miniature an exact copy of Axle is prooving difficult, mostly due to sunglasses and the leather jacket.  So now I am wondering how big should a puppet be for a GSP to look like a normal puppet?  Hope that makes sense

Sounds like you need to think in terms of scales and ratios. Reminds me of this:
https://m.flickr.com/#/photos/schoolofpuppetry/3880915286/in/set-72157622087845129/

:D  That looks about right!  The current plan is for Tyger to have a detachable left arm for his regular arm and his puppet arm.  The puppet arm will be a mechanism that I can control with my left hand, for mouth and head movements.  Sizing only becomes a problem because when Tyger isn't in the shot, it will be me controlling his puppet normally (since Tyger wants to flim puppets).  Sizing the pattern isn't difficult, sizing the extras is, especially if I keep the Axle puppet.  The easy way, of course, is to size Tyger up to where a full size GSP looks like a puppet and not..uhm...a colleague.

I am not entirely sure what you mean but for the most part again it comes back to scales and ratios. Measure the real life objects, then figure out the size you need for one of the smaller ones. Use a scale conversion to figure out 'if x is needed, then y should be...?'

Ie. if you use 1:25, where 1 is a foot and 25 is inches, then your 6 foot puppet needs to be x inches tall. Dont have a link handy but there is a scale conversion calculator out there so you dont need to do the math. A scale ruler and some sketches might help you visualise it better and adjust measurements before building.