Posting the Sears 917.xxxxxx or similar number would allow someone else to actually look at the schematic if available.

There's probably at least a dozen implementations of safety switches on Craftsman tractors.
One CANNOT assume if they are NO or NC without the schematic.
At least not on this side of the internet.

Bill, it is a 536.270282 Mid-Engine Rider. I have attached a scan of the electrical system diagram from the manual.
I also re-checked the switches, because my original post seemed wrong in light of the diagram. Sure enough, my original post was wrong.
The seat switch is closed when there is no weight on the seat, and goes open with weight. The blade switch is closed when blade is disengaged and goes open when engaged. The clutch switch is different: it is open when clutch is up, and closed when clutch is depressed.
The diagram shows both the clutch switch and the blade switch as four-pole switches, but the actual switches in the machine each just have two spade terminals.
Thanks for the response and I hope the additional and corrected information helps!
Lewis

I just downloaded the manual so the schematic is more legible-

Anything that grounds the YELLOW (kill) wire will prevent spark.

One thing to check is the seat switch connector. Some have a "shorting tab" which will still complete the connection even if the plug is pulled.
The clutch/brake & attachment (blade) switch are dual switches. You have to make sure you are checking the proper "side".
ORANGE wire is the crank circuit.

Here's a page from a manual of a mower with a slightly different part number, but that looks just like mine (on the cover shot of the manual). This one shows the clutch switch as a simple 2P NO switch, which seems to correspond to my mower.

Both diagrams show the blade/PTO switch to be NO on the orange wires. My mower only has orange wires to this switch, and it is normally closed. I'm thinking this is the problem switch.
Lewis

here is the diagram I referenced in my last post

The PTO diagram doesn't match what they are saying.
The kill circuit is open when disengaged, since you aren't "in danger" when the blades aren't spinning.
The crank circuit is closed when the blades are disengaged, since you don't want to be turning the blades when trying to start the engine.

Don't overlook testing the key switch too.
The kill circuit operates with each switch connected in a 'parallel wired" configuration, meaning that any single switch closes and the kill wire to the coil becomes grounded if the seat switch is closed. The key switch kill wire has its own separate ground and will kill the engine even if the other switches are open.
The crank circuit in contrast is "series wired" so each switch must be closed before the starter solenoid gets its signal to start.
Having unplugged the kill wire from the coil you still need to check each switch that has the yellow wire in it, and with it in the proper "mode of operation".
Clutch pedal must be up and the switch show continuity, no continuity when down.
PTO must be engaged and the switch show continuity, no continuity when disengaged.
The seat switch should show continuity when seat is empty, no continuity when seat is occupied.
The key switch kill function can be tested by removing the wires from the switch and testing between key switch terminals M and G. With key OFF, there should be continuity between M&G. With key in RUN, there should NOT be continuity between M&G.

Between your responses and the partly-applicable diagrams, I think I'm starting to get it. In this mower, unlike the diagrams I'm looking at, there are no yellow wires to either clutch or PTO, only orange. Both switches on the orange circuit need to be closed for the motor to start, correct? So the blade/PTO switch should be closed only when the blade/PTO is disengaged. And the clutch switch should be closed only when the clutch is depressed. Which is the way they are working now. So those two seem OK, right?

Mownie,
That's a great plan of attack!
Thanks,
Lewis

mownie got it! I unplugged the seat switch to troubleshoot the electrical and the dam plug was shorted...snipped one wire and soldered in a single M/F connector for future troubleshooting...going to replace switch...eventually...Thank You!