It does sound electrical. The engage switch could be internally oxidized and not making contact every time. A little WD 40 squirted on/in it won't hurt. Then exercise it a bunch of times. If you hear any noise underneath when you flip the switch, it could be the clutch not engaging (I don't know if the clutch will operate with the engine off or not ... quieter). It could be a bit sticky from rust or dirt. If you have a volt meter you can proceed through the system to see what is or isn't happening. A mallet might lead you to the problem. Tap on the switch, clutch, etc. to see if you can narrow it down, by determining which area helps.

Check the various safety interlock switches. Seat switch first. Check the electric PTO connector (under the tractor). If you have a few seasons on it, your clutch may require an adjustment (assuming it's an adjustable one). The gap between the clutch plates opens up with use. A wide gap can translate into inconsistent clutch engagement (appears like an electrical problem). My Simplicity needed a clutch adjustment after about the first 150 hr. Seat switch connector was a little loose too (zip tie to keep plug firmly seated in connector). Symptoms just as you described. Your manual will have intructions for clutch adjustment.

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