Holy Schni-kees, Batman!! Roland you are correct: the 1811 is certainly wired differently than either style 782, and the two versions of the 1811 are wired more differently from each other than they are from either of the 782s, although its development can be traced across all four models.
The earlier 1811s, before S/N 757,000, are wired a lot like the later 782 models, except that they use a Seat Relay to ground out the magneto. The Seat Switch itself is Normally Closed, unlike the earlier 782 or the later 1811s (757,00 and later). The Seat Relay is energized by the the RELEASE of the Seat Switch, and the Seat Relay, when energized grounds out, or "kills," the magneto.
Note that the Seat Switch itself gets its power from the N/O terminal of the Reverse Relay, which in turn is fed by the "R" (Alternator) terminal at the key. This arrangement places the Reverse Relay in SERIES with the Seat Relay --both the Seat and the Reverse circuits are needed for the tractor to run or the PTO to operate. The PTO itself is dropped when the N/C Reverse Switch trips the "latch." See below:
The later model 1811s implements the same logic for the Seat and Reverse circuits in a much simpler fashion: a N/O Seat Switch is simply inserted in the latch in series with the N/C Reverse switch. In this arrangement, getting out of the seat no longer shuts off the motor: it simply drops out the PTO, which seems like a much saner arrangement to me.
I hate it when the seat switch kills the motor, even though I know that its purpose is to preserve my safety.
So, thank you Roland for giving me the opportunity to educate myself, and hopefully give Charles some proper guidance for his 1811. I apologize to all for muddying the waters. I have always had a hard time staying on topic (a fault some owner/moderators have occasionally pointed out).
Charles, if you can't find a serial number on the tractor, one way to answer Roland's question is to check to see how many relays are on your tractor; if you find two it is an earlier version of the 1811, if you only find one (and no tell-tale wire harness butchering) you likely have the later version.