A fully charger 12v battery should test at 12.7v-12.9v. The charging system by way of the voltage regulator should be testing between 13 and 16 volts, dependant on what the battery needs. 16v seems high to me, but that's what I was taught in a class. Normal high to me is 14.5v. Anyway,
This is my issue. Mine does this exact same thing. You turn the key to start it and you hear the starter click but it does engage. It is especially noticeable if I realize that it isn't going to start and I need to let off the key to choke the mower. Usually if I give it some time or several attempts as you mention it will then engage.
I am seriously thinking about wiring a push button starter and toggle switch to my control board. That would be really convenient for me because of how often I need to turn the mower on and off. It would also eliminate the problem of stuff getting snagged on it like you mentioned which undoubtedly played a part in my ignition switches undoing. Watching people wire them sort of makes me uncomfortable though. Because it looks like you do have to leave the original wires intact and only tie into them to install the starter.
Thanks for the input!
I'm betting your starter relay is giving you fits. They are inexpensive, but as they get older, they work great with fresh batteries, but when the battery gets a little age, the slightest voltage drop will make them fail. At my last job, I had a dozen on the shelf every spring, and usually ordered more. Over 12 years, I figured the one OE brand wasn't good, I'd try another. Turns out, all the OE are the same quality. I fixed my personal mower with a White-Rodgers relay, P/N 586-902. I also put the same relay on three different Ford Powerstroke trucks as a glow plug relay, because OE and aftermarket relays only last about a year. Two of those trucks had these on for 4-5 years before the truck was sold. The third truck is my father in laws, and it has been on there for 19 years. So after all that testimony, for ease, you can replace the original one with a like relay, Napa #7018611, around $35, or the other I listed for a little more, just may need a little mounting modification, but your wires should reach. A mower dealer may have one cheaper than Napa, I was buying OE direct from Husky, Ferris, Xmark etc. for around $15 and selling them at $17.