The solenoid should not affect spark. The harness to it and the associated micro switch could if shorted.
You would generally test an M-tronic control module for spark just like any coil. Pop the M-tronic connector loose from the module, short the plug to the cylinder and spin the flywheel. No spark, bad module 99% of the time. That said, I've found two instances of the plug lead being rubbed through in the case channel on 661s which created a direct short to the case. You may want to check that 261 for a similar condition.
The sticker on the rear handle foot pad may indicate the version of M-tronic which will in turn affect the version of module recommended as a replacement (if necessary). If you don't have a MS261 C-M IPL I can hook you up. I don't remember if I sent one. I can also forward some other random M-tronic material that may come in handy down the road.