Starting problem, advice before I plunge in?

[kongjie]

The other day after work I got on the bike, thumbed the starter and nothing happened. Lights didn't dim so it seemed like the battery was not the issue. I push started it in second and it started right up.

That morning when I rode in, it was raining heavily. I'm in NorCal and this has been a particularly wet time.

At home I shut off the bike, hit the starter and it worked fine.

Couple days later it happened again. Can't remember the weather conditions. But what I do remember is that I went to push start it but it was in first, so didn't work first shot. On an impulse I thumbed the starter and this time it turned over and started.

I've seen this at least one more time: the starter doesn't work the first time, I bump it, the starter works fine.

So before I start checking everything with a multimeter, any suggestions re: what I should focus on?

Two other bits of info that are probably not related but I mention them anyway: 1) week ago I adjusted the valves, and 2) some weeks ago the neutral light started working erratically and then just stopped working at all.