No way would i be pulling the starter just yet. Need to test, not guess. The only advice i agree with is from ArmedsouthernER. If there was a short to ground you would blow a fuse and it would stop clicking at all. Lights are going dim due to voltage drop while attempting to crank engine – again most likely not due to a short to ground. (One thing I am not clear about is what you are saying battery voltage is after charging. Is it holding 12v or so while cranking after charging?. Or if voltage drops fast to 9v or lower you may simply have a battery issue. I’m assuming from here on out battery is good.)
First thing is to check all the easy/basic stuff. namely battery terminal connections and starter connections and ground connections. This usually finds the issue.
Like what ArmedsouthernER said, you can check for solenoid control voltage at starter to make sure it is getting power, but from sound of clicking in vid it is. If not, you need to trace down where open is in that control wire circuit. If control is ok, move to below steps.
You noted the battery was 9v in the morning so obviously something drained the battery overnight. That is A problem but may not be THE problem. If voltage is staying up across battery posts during cranking after charging then deal with parasitic draw later.
The way I like to test starter is check voltage between battery posts (and i mean DMM leads on posts, NOT terminals. Being on terminals i got wrong diagnosis once) while cranking. If voltage stays above around 10V, then repeat tests across starter. Red lead on main big power feed post (again NOT terminal but on post ) of starter, black lead to starter housing bolt (clear of paint, grease grime etc. need a good ground connection). crank engine. If voltage drop is the same reading as across battery (10v or above), then starter/solenoid is bad and needs to be replaced. (with only possible exceptions to this being a seized engine or seized accessory like an alternator that is preventing starter from turning engine. But again from sound of video these don’t at all sound likely)
If voltage drop is a lot lower across starter – say 6v, then you have a wiring problem. Move black lead you have on starter housing to battery negative post (not terminal) and repeat cranking. If voltage drop goes back to same reading as across battery ( >= 10v), you have a grounding wire problem between battery and starter. If voltage still drops low, problem is on power feed side. From here you trace the path from battery to power/ground connections taking voltage drop readings along the way to find where the unwanted drop is.
I hope this makes sense.