Solenoid Issue?

[Duggo]

After sitting for a month, with the keys out, the battery was dead. Why? It should sit for months with the keys out, especially in the summer.

I may have left the headlight on and I have twin boys, things happen mysteriously at my house.

We kicked started it and it ran fine yesterday. I charged the battery.

Today, I put the 100% battery in and now the "solenoid? see pic" is clicking and the starter won't engage.

Between the government bullshit just to ride it, and the battery dying, and now the solenoid being wrong, I'm a little pissed off. I didn't try to kickstart it, but I'm sure it will run.

What am I doing wrong?

I don't see how I could have worn out the solenoid. The bike has about 30 miles on it. Maybe it got started 30 times.