You do need a switched live to the bat terminal, but not to the tach terminal. The tach terminal is the negative side of the coil, the bat terminal is the positive side of the coil. Normally the tach terminal is for the green wire from the tach.
The purple wire would attach to the terminal marked "S". this terminal would be the one closer to the engine block. The yellow wire would attach to the terminal marked "R". This terminal would be the one further from the block.