If I'm not mistaken, you have started different threads for the same issue (intermittent start from the control switch). I can't sort that out but give this a try with the bike in neutral. First , pull the green wire off the starter solenoid. Second , put a meter to ground on the connector. Third, turn the key on and hit run then start. You should get 12vdc on the green wire along with hearing the click from the Compression Releases. Repeat a bunch of times because you have an intermittent problem. When it fails I suspect you will hear the click from the CR's but not get the 12 vdc on the wire. If you do it 10 times and always get the 12vdc and the click, your issue is most likely with the Solenoid.
If you get the intermittent failure (no 12vdc ) your issue is with the EHC and not the Solenoid. If this is the case pull the connectors off the EHC looking for a loose or backed out wire then replace the Dielectric grease and put it all back together.
Come back with your findings and avoid starting new threads because it makes it difficult to help you.