Thanks for asking and trying to reconcile with TGM. Good news and bad news I'm afraid.
Downstroke Waggle and Horizontal Hinging are the distant TGM cousins of your drills.
But those drills are just a part of the whole for each. In other words, they are incomplete. But you can learn a few things from them.
The most valuable thing in the pump drill is seeing the plane, assuming your instructor told you to point the butt of the club at the base of the plane. That will be the path of the right shoulder and hands downplane. The problem with the drill is that it ignores the total motion, that of the pivot and release point.
The arm roll drill is the feel of horizontal hinge roll, and follow-through swivel. If you are holding the left wrist from it's natural swivel, then this might help give you the feel of it. It's a bandage rather than finding the cure because horizontal hinging is the natural bi-product of a centrifigal force swing.
Forcing a horizontal hinge can result in hooking the ball among other things, such as engraining a faulty pivot.
Both of these drills are semi-helpful but can also be semi-harmful.
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