Context Menu Pops Up With Every Cursor Move, Without Right Click

Windows 10, Fall Update, 1809 190119-1759, also 1803 & 1806. Dell Optiplex 745 & 760.
This happens in Firefox, Nightly & Thunderrbird when changing tabs and filling forms. Left click anywhere , like selecting an email to open or delete and the menu pops up.
Partifularly irritating in Babas Chess! When I move a piece, the menu pops up.
Sometimes when my opponent moves. It obscures the view of board & pieces.

Tried & failed: replace generic mouse & kbd., mouse settings, safe mode, clean reinstallation, ASC12 & Tweraking.com Windows Repair.

Yes.

Did you, somehow, swap left/right mouse buttons...

No! Swap was never checked. I would only do that if muy index finger was extremely sore.

Only an external hard disk; removing it makes no difference.

AddRAM said:

Did you look in Programs & Features ?

Maybe you accidentally installed something.

This is a clean reinstallation of Windows & updates, no change in the mouse behavior.