"I take the square wave as the heating element. Odd, but it seems they also have some resistance built into the circuit too??
The schematic portion of the seat heating pad is vague. "the block" shows Power-in (Green), Ground (White-Black), and Control (Purple). We see wire routing inside the seat and wire routing "to" the seat but there's a missing void between the two that might connect the circuit of how solid positive power and control interact.
Guess 1: Solid power in is used to activate a "person present" (there's a person sitting in the seat) circuit with a pressure switch / relay (that small I - beam item on the heating circuit). Once the person present circuit is happy it is then capable of passing controlled power to the heating elements - either with pulse width modulated control or via variable resistor control. In this case, I should think you could give the seat 12vDC, 100% on positive power to Green and Purple and ground to White-Black. With pressure on the seat, closing the "there's a person here, warm the seat up", it should get hot.
From there, you'll want to "control" how much power goes into the heating elements (via purple) so that you don't get uncomfortably hot.
EDIT:
Guess 2: Leave Green disconnected. Supply 12vDC power to Purple and Ground to White-black. Sit on the seat to activate a pressure switch / person present - and see if it warms up. If yes, Green is not needed / I don't know what it is for. Again, modulate / control power input on Purple to not have 100% heating.
I started to draw the schematic (edit from the screen shot) and I scratch my head as to what the item on the far right (in the seat) is. The I-beam I take as person present switch / circuit completion for heating.
As an aside, looking at the controller circuit - something you don't have (I assume) - it looks like the controller circuit has On/Off toggle and when on there's an LED giving off illumination to indicate ON status and that the heating control has only two positions - Low and High.
Have you decided on how you wish to control heat amount to the seat? The heat trollers could work (but a bit pricey) or you could make an 555 timer circuit with a rheostat.
http://www.555-timer-circuits.com/"
So are u fairly certain about the "I" being person present? I have the leather partially peeled back off of the foam at the front of the lower cushion. I have connected power to green and ground to ground on my jumper box with nothing happening. But I didn't sit in the seat. Could the person present contact actually be in the heating pad? Thanks for your help by the way. Haven't gotten into control too much yet. Waiting till I can get the pads to actually work first.