Rob's diagram shows what you need to know but I already made this diagram for a previous thread albeit for the Realtrax operating track. In this case MTH used a sealed standard (ON)-OFF-(ON) DPDT toggle rather than the "brass tab" style apparently used in some controllers. I found it somewhat amusing how they fabricated custom mechanical parts to maintain the look and feel of a traditional O-gauge lever controller mechanism with a "modern" toggle switch buried within!
The WTS-6303 appears to be a Korean company with a 125V/3A rating...a functionality readily available in switches that cost, say, $2-3.
Or, to your point, separate the integrated toggle into separate doorbell-style pushbutton switches.