Figured it out by taking apart the new switch, finding where the two bimetals were, and then tracing the line 1 (P1)and 2 (P2) through the switch.

2 goes to the brown wire
P1 is the black wire off the other switch (Line 1)
P2 is the thick red wire off the other switch (Line 2)
4 thin red wire from the inside element
4a thin orange wire from the outside element
S2 is the thick red wire that goes to the "ON" indicator light

And there you have it!
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