Hi Shortgrass24, and welcome to TGMF
Those Honda's are notorious for coils dying, but like you said not normally both at the same time unless there was a major wiring fault on the machine.
As you said, the thin wire from each coil does the job of stopping the engine when grounded. That wire is split into three via a diode module between the coils.
The engines are also very fussy on spark plugs, I have seen plugs that spark on one engine and not on another. So if it hasn't had a new set for a while I would try that first before throwing money at coils. Also make sure it's getting fuel, especially as it's not been run for so long.
Those Honda's are notorious for coils dying, but like you said not normally both at the same time unless there was a major wiring fault on the machine.
As you said, the thin wire from each coil does the job of stopping the engine when grounded. That wire is split into three via a diode module between the coils.
The engines are also very fussy on spark plugs, I have seen plugs that spark on one engine and not on another. So if it hasn't had a new set for a while I would try that first before throwing money at coils. Also make sure it's getting fuel, especially as it's not been run for so long.