Once I received the new pick-up coil, I put my digital meter on it to see if it would show any resistance. It, as well as the old one, did not. I switched the meter over to 200k (I think), and it did show resistance of like .005 or something. Placed same on old pick-up, and it too read the same reading. Attempted to heat old pick-up, no change, still read same resistance as the new one. Was convinced this too wouldn't fix my bike.
Went ahead and installed the new one after measuring original gap, replaced gasket, and she fired right up, and ran as stated above.
Parked bike until new Triumph shop manual arrives Wednesday to make sure pick-up coil is installed correctly.